Questions on Algebra: Probability and statistics answered by real tutors!

Tutors Answer Your Questions about Probability-and-statistics (FREE)

Question 571389: The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000.
112,000 126,000 90,000 133,000 94,000
112,000 98,000 82,000 147,000 182,000
86,000 105,000 140,000 94,000 126,000
119,000 98,000 154,000 78,000 119,000

Answer by stanbon(48510)

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Ans: 13/20

Question 571407: Ted performed an experiment which he placed 10 colored marbles into a bag. He then reached in,picked a marble,recorded his color,and replaced it in the bag.He did this a 100 times,and his results were; brown 29,gray 42,green 10,and purple 19. What was the experimental probability of picking a gray marble? 1/42,21/100,2/5,or 21/50.Also what was the theoretical probability of choosing a brown marble? 1/10,2/9,3/10,or 1/2.
Answer by stanbon(48510)

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Ted performed an experiment which he placed 10 colored marbles into a bag. He then reached in,picked a marble,recorded his color,and replaced it in the bag.
He did this a 100 times,and his results were; brown 29,gray 42,green 10,and purple 19.
What was the experimental probability of picking a gray marble?
Ans: Based on his results: 42/100 = 21/50
------------
1/42,21/100,2/5,or 21/50.
========================================
Also what was the theoretical probability of choosing a brown marble? 1/10,2/9,3/10,or 1/2.
---
You can't tell the teoretical probability of brown because you do
not know how many of the 10 marbles are brown.
However, the experimental probability of brown is 29/100
=====================================
Cheers,
Stan H.
===============

Question 571283: How do you find the smallest power of 0.917 that yields a value less than 0.10. The answer book says 27 (rounded up). How did they get that?
Found 3 solutions by lwsshak3, unlockmath, scott8148:
Answer by lwsshak3(2915)   (Show Source):
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How do you find the smallest power of 0.917 that yields a value less than 0.10. The answer book says 27 (rounded up). How did they get that.
**
.917^x<0.10
Take log of both sides
xlog(.917) divide both sides by log(.917) and reverse inequality signs (note: both logs<0)
x>log(0.10)/log(.917)
Using calculator
x>26.574..
The smallest power of 0.917 that yields a value less than 0.10≈27

Answer by unlockmath(1120)   (Show Source):
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Hello,
Let's set this up as:
.917^x=.10
If you have a scientific calculator we can set up:
Log(.917).10=x (Note: .917 is subscript or base)
x=26.574 round this up to 27
Make sense?
RJ
www.math-unlock.com

Answer by scott8148(5879)   (Show Source):
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x log(.917) < -1

Question 570867: A company brings a new product to market:
The probability of loosing $1,000,000 is 10%
The probability of loosing $500,000 is 20%
The probability of breaking even is 20%
The probability of making $500,000 profit is 20%
The probability of making $2,000,000 profit is 30%
what is the expected profit?
I can calculate this ((2,000,000*.3)+(500000*.2)) - ((1,000,000*.1)+(500,000*.2))
yields 700,000-200000 = $500,000 expected profit. but im not sure how to handle the 20% probability of breaking even, 0 * 20% = 0? how is this factored in to my calculations?
Answer by richard1234(4789)   (Show Source):
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Do it just like you did with the other numbers. Expected value for this problem is defined as the sum of (profit)*(probability of that profit), so with the case of zero profit, you would add 0*.2, or 0. Since your other numbers are correct, you can just add everything and obtain $500,000.

Question 570976: Suppose k identical boxes contained n balls numbered one through n. One ball is drawn from
each box. What is the probability that m is the largest number drawn?

Answer by richard1234(4789)   (Show Source):
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For this problem we will assume that .

The best way is probably to try small cases (for m). Let P(m) be the probability that m is the largest number drawn. If m = 1, then every number drawn must be a 1, and

If m = 2, every number must be a 1 or a 2, and we would try to claim something like

However, this is incorrect, because this includes the case where every number is a 1 (which violates the constraint that at least one number must be a 2). To fix this, we subtract P(1):

Finding P(3) is similar to finding P(2), except that we subtract P(2):

This generalizes to

, or

where the plus/minus of (1/n)^k depends on the parity of m (i.e. if m is odd, +; if m is even, -).

Question 571054: You are asked by the owner of the Starshine Motel to develop a customer satisfaction survey to determine the percentage of customers who are dissatisfied with service. In the past year, 20,000 customers were serviced. She desires a 95% level of confidence with an allowable statistical error of +/- 0.02. From past estimates, the manager believes that about 4% of customers have expressed dissatisfaction. What sample size should you use for this survey?
Answer by stanbon(48510)   (Show Source):
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You are asked by the owner of the Starshine Motel to develop a customer satisfaction survey to determine the percentage of customers who are dissatisfied with service. In the past year, 20,000 customers were serviced. She desires a 95% level of confidence with an allowable statistical error of +/- 0.02. From past estimates, the manager believes that about 4% of customers have expressed dissatisfaction. What sample size should you use for this survey?
----
n = [Z/E]^2*p*q
------
n = [1.96/0.02]^2*0.04*0.96 = 369
===================
Cheers,
Stan H.

Question 571022: The spinner below is spun twice. Find the probablity of the outcome numbers 1-8. Find the P(a number less than 3 or a number greater than 5)
Answer by nyc_function(2626)   (Show Source):
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Let event A = probability of a number less than 3.
Let event B = probability of a number greater than 5.

P(A or B) = P(A) + P(B)

Let A = (# < 3) = 2/8
Let B = (# > 5) = 3/8

Plug into formula above and add.
Can you finish now?

http://www.youtube.com/watch?v=VzfqzqVmRmU

Question 570991: Hello. Guys, I really need your help on this one please
Below are the home states of 16 college professors..

Florida Indiana Pennsylvania Arizona Georgia
Florida Tennessee Texas Kansas Arizona
Texas Florida Tennessee Arizona Texas
Indiana

a)Make a frequency table using these 8 states:
Arizona Kansas
Florida Pennsylvania
Georgia Tennessee
Indiana Texas

b)What is (are) the mode(s)?
c)Does it make sense to talk about the average for this data? Why or why not?

Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(21667)   (Show Source):
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a)

Simply create a two column table in which the names of the states are on the left side and the respective counts are on the right

For example, the state "Arizona" occurs 3 times in the list, so write a "3" next to "Arizona" in the table. Do the same for the rest to get

State | Frequency -------------------------------------------------------- Arizona | 3 Florida | 3 Georgia | 2 Indiana | 1 Kansas | 1 Pennsylvania | 2 Tennessee | 1 Texas | 3

-------------------------------------------------------
b)
The mode is the value that occurs the most. In this case, the modes (you can have more than one mode) are Arizona, Florida, and Texas since they all occur three times (the most of any other state)

-------------------------------------------------------
c)
It does NOT make sense to talk about the average because this data is NOT quantitative. So you cannot add up the states names and divide them by 16 because adding is not defined when it comes to names (eg: what is Texas + Kansas equal?). So there is no average state

Note: when people say "average", they usually refer to the mean.

Answer by Edwin McCravy(6931)   (Show Source):
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Hello. Guys, I really need your help on this one please Below are the home states of 16 college professors.. Florida Indiana Pennsylvania Arizona Georgia Florida Tennessee Texas Kansas Arizona Texas Florida Tennessee Arizona Texas Indiana a)Make a frequency table using these 8 states: Just count how many times each state is listed above. For instance, Florida is listed 3 times, Indiana is listed 2 times, etc. State Frequency Arizona 3 Florida 3 Georgia 1 Indiana 2 Kassas 1 Pennsylvania 1 Tennessee 2 Texas 3 b)What is (are) the mode(s)? The first three letters of the word MOde are "MO" and the first three letters of the word MOst are also "MO". So that's a way to remember that MODE means MOST. There are three states with the MOST professors, so there are three MODES: Arizona, Florida and Texas. c)Does it make sense to talk about the average for this data? Why or why not? No because states are not numbers. Average number per state in no good either because all 50 states are not listed. Edwin

Question 570982: what are 5 multiple choice about basketball

Answer by JBarnum(1826)   (Show Source):
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???
1) requires an inflated ball
2) shorts are required
3) slam dunks are allowed
4) penalty shots
5) requires a basket(hoop)

Question 570980: Provide a written description of the complement of the given event.
Of the thirteen different women Calvin asks for a date, at least one of them accepts.
Answer by jim_thompson5910(21667)   (Show Source):
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The complement of an event is simply the polar opposite of the given event.

Given: Of the thirteen different women Calvin asks for a date, at least one of them accepts.

Complement: Of the thirteen different women Calvin asks for a date, none of them accepts.

Question 570941: Question:
A single dice is rolled 2 times. What is the probability that the next roll will produce a number less than 3?
Answer by stanbon(48510)   (Show Source):
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Question:
A single dice is rolled 2 times. What is the probability that the next roll will produce a number less than 3?
-----------
The results on each roll are independent.
# of results < 3: 2
# of random results: 6
---
P(result < 3) = 2/6 = 1/3

Question 570978: if an apple is hanging from a string and 3 flies land on it, find the probability that all 3 are on points that are within the same hemisphere
Answer by stanbon(48510)   (Show Source):
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if an apple is hanging from a string and 3 flies land on it, find the probability that all 3 are on points that are within the same hemisphere
----------
Binomial Problem with n = 3 and p(same) = 1/2
----
P(x = 3) = (1/2)^3 = 1/8
===========
cheers,
Stan H.

Question 570967: The product of 3! and 4! is
Answer by jim_thompson5910(21667)   (Show Source):
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3!*4! = (3*2*1)*(4*3*2*1) = (6)*(24) = 144

So 3!*4! = 144

Question 570955: suppose A and b are events such that P(A)=1/3, P(B)= 1/3, and P(Aor B)=1/2. complete parts (a) and (b) below.
a. are events A and B mutually exclusive ? explain your answer.
b. determine P(A &B).
P(A& B) = ?
Answer by jim_thompson5910(21667)   (Show Source):
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a)
Two events A and B are mutually exclusive when P(A or B) = P(A) + P(B).

So let's plug in the given values to see if that's indeed true.

P(A or B) = P(A) + P(B)

1/2 = 1/3 + 1/3

1/2 = 2/3

This is false, so the events are NOT mutually exclusive
-------------------------------------------------------
b)
The formula given above really expands to

P(A or B) = P(A) + P(B) - P(A & B)

and you can solve for P(A & B) to get

P(A & B) = P(A) + P(B) - P(A or B)
------------
So plug in the given values to get...

P(A & B) = P(A) + P(B) - P(A or B)

P(A & B) = 1/3 + 1/3 - 1/2

P(A & B) = 2/3 - 1/2

P(A & B) = 4/6 - 3/6

P(A & B) = 1/6

Question 570953: Any help on a true false question these are very tricky for me.
1) A regression line was calculated as y = 9.7 - 3.2x. The slope of this line is -3.2 True or False
Eric
Answer by jim_thompson5910(21667)   (Show Source):
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This is true because the general equation of a line is y = mx+b where m is the slope. It takes a bit of rearranging, but y = 9.7 - 3.2x can be restated as y = -3.2x+9.7 and we can see that m = -3.2

Question 570950: I am having a difficult time finding the answer to this question any help would be greatly appreciated.

1) A correlation coefficient of 0.96 would mean that the values of x increase as the values of y decrease. True or False
Eric
Answer by jim_thompson5910(21667)   (Show Source):
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This is false since the correlation coefficient is positive and very close to 1. A positive correlation means that as x increases, y increases. Also a positive correlation means that as x decreases, y decreases.

The true statement would be "A correlation coefficient of 0.96 would mean that the values of x increase as the values of y increase"

Question 570879: if 8 students have blue eyes and 4 has brown, whats the percentage of blue eyes
Answer by maa.veera@gmail.com(3)   (Show Source):
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Number of students with blue eyes = 8
Number of students with brown eyes= 4
Total number of students = 12
percentage of blue eyes = number of blue eyes students/Total students x 100

= 8/12 x 100
= 66.67 %

Question 570845: Find the probability that when you roll two dice, the sum of the outcomes is greater than 6 or you get a 5 on one of the dice?

Thank you
Answer by Edwin McCravy(6931)   (Show Source):
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Here's the sample space: ⚀⚀ ⚀⚁ ⚀⚂ ⚀⚃ ⚀⚄ ⚀⚅ ⚁⚀ ⚁⚁ ⚁⚂ ⚁⚃ ⚁⚄ ⚁⚅ ⚂⚀ ⚂⚁ ⚂⚂ ⚂⚃ ⚂⚄ ⚂⚅ ⚃⚀ ⚃⚁ ⚃⚂ ⚃⚃ ⚃⚄ ⚃⚅ ⚄⚀ ⚄⚁ ⚄⚂ ⚄⚃ ⚄⚄ ⚄⚅ ⚅⚀ ⚅⚁ ⚅⚂ ⚅⚃ ⚅⚄ ⚅⚅
Count the red ones. There are 23. That's 23 out of 36, so the probability you want is Edwin

Question 570854: If you toss a coin and randomly select a number from 0-9, what is the probality of getting tails and selecting a 3
Answer by Edwin McCravy(6931)   (Show Source):
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Sample space: {H&0, H&1, H&2, H&3, H&4, H&5, H&6, H&7, H&8, H&9, T&0, T&1, T&2, T&3, T&4, T&5, T&6, T&7, T&8, T&9} That's 1 way out of 20 or a probability of Edwin

Question 570661: what is the probability of a person is between the ages of 40 and 49?
Answer by richard1234(4789)   (Show Source):
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Depends on the distribution of ages in your population.

Question 570761: Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no knowledge of the approximate value of the sample proportion.
Answer by richard1234(4789)   (Show Source):
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, where z = 1.645, E = .03, assume p = .5 because this maximizes p(1-p) and we want a safe estimate. Plugging in everything, we obtain

A sample size of 752 would work.

Question 570682: A multiple choice quiz consists of five questions, each with three possible answers of which only one is correct. a student passes the quiz if three of more correct answer are obtained. what is the probability of a student passing the quiz by randomly guessing the answer to each question
Answer by stanbon(48510)   (Show Source):
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A multiple choice quiz consists of five questions, each with three possible answers of which only one is correct. a student passes the quiz if three of more correct answer are obtained. what is the probability of a student passing the quiz by randomly guessing the answer to each question
----------------------
Binomial Problem with n = 5 and p(correct) = 1/3
---
P(3<= x <=5) = 1 - binomcdf(5,1/3,2) = 1 - 0.7901 = 0.2099
====================
Cheers,
Stan H.
==================

Question 570689: A standard poker deck of cards contains 52 cards, of which four are queens. Suppose two cards are drawn sequentially, so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. Find the probability that the first card is a queen and the second card is not a queen. (Enter your answer as a fraction.)

Answer by stanbon(48510)   (Show Source):
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Suppose two cards are drawn sequentially, so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. Find the probability that the first card is a queen and the second card is not a queen.
-----
Ans: (4/52)(3/51) = 0.0045
================
Cheers,
Stan H.
=============

Question 570240: Below are the home states of 21 college professors.
New Jersey Ohio Michigan South Carolina Nebraska
South Carolina Ohio South Carolina Pennsylvania Michigan
Georgia New Jersey Wisconsin Georgia Ohio
Florida Georgia New Jersey South Carolina Wisconsin
Pennsylvania
i. Make a frequency table using these 9 states:
Florida
Georgia
Michigan
Nebraska
New Jersey
Ohio
Pennsylvania
South Carolina
Wisconsin
ii. What is (are) the mode(s)?
iii. Does it make sense to talk about the average for this data? Why or why not?
iv. Using your frequency table draw a pie chart to display the distribution of home states by filling in the following table:
Home State Frequency Percentage of Measure of Central
total Angle (in degrees)
Florida
Georgia
Michigan
Nebraska
New Jersey
Ohio
Pennsylvania
South Carolina
Wisconsin
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
i. Make a frequency table using these 9 states:

State | Frequency ------------------------------------------------------- Florida | 1 Georgia | 3 Michigan | 2 Nebraska | 1 New Jersey | 3 Ohio | 3 Pennsylvania | 2 South Carolina | 4 Wisconsin | 2

All you do here is write the name of the state in the left column and count how many times you see it and write that count in the right column.

==============================================================================

ii. What is (are) the mode(s)?

The mode is the data element that repeats/occurs the most. So the mode is South Carolina since it occurs the most at 4.

==============================================================================

iii. Does it make sense to talk about the average for this data? Why or why not?

Since the data is NOT quantitative (it's qualitative), you cannot average the data because it doesn't make sense to average names of states. If it were possible, then what is the average of Georgia and Pennsylvania? Is it a state? If so, then is it some state between the two states? If that's the case, then what's the average of Georgia and Florida? So we can see this hypothetical "average" breaking down quickly. So it does NOT make sense to talk about the average for this data.

==============================================================================
iv. Using your frequency table draw a pie chart to display the distribution of home states by filling in the following table:

I'll let you take this one. All you need to do is enter the data into some spreadsheet program (like excel) and it will create the chart for you.

Question 570023: Amy has a quiz on which she has to answer any 3 out of 5 questions. If she is equally well versed on all questions and chooses at random, what is the probability that 1 is not chosen?
Answer by stanbon(48510)   (Show Source):
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Amy has a quiz on which she has to answer any 3 out of 5 questions. If she is equally well versed on all questions and chooses at random, what is the probability that 1 is not chosen?
-----
@ of ways to succeed: 4C3 = 4
---
# of random drawings of three: 5C3 = 5C2 = 10
----
Ans: 4/10 = 2/5
====================
cheers,
Stan H.
=====================

Question 570033: what is the value of determinent if entries in any two rows of the determinent are crrespondingly proportional
Answer by stanbon(48510)   (Show Source):
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what is the value of determinent if entries in any two rows of the determinent are crrespondingly proportional
---
That condition implies two equations are actually the same.
So there is an infinite set of solutions.
So, for example, Dx/D = Dx/0
---
So the coefficient determinant is zero.
====================
Another way to look at it:
Using row operations you can create a row with all elements = 0.
Therefore the determinant will be zero.
===========================================
Cheers,
Stan H.

Question 569955: The Thomas Supply Company, Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of The Thomas Supply Company, Inc. invoices.
13 13 13 20 26 29 31 33 34 34 35 35 36 37 38 41 41 41 45 45 47 47 48
52 54 56 56 62 67 82

(a) Determine the second decile and the eighth decile.

D2 =
D8 =

(b) Determine the 67th percentile.
Answer by stanbon(48510)   (Show Source):
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13 13 13 20 26 29 31 33 34 34 35 35 36 37 38 41 41 41 45 45 47 47 48
52 54 56 56 62 67 82
-----
Note: There are 30 elements
(a) Determine the second decile
Locator: 0.20*30 = 6
Round up to 7
20%ile = 31
-----------------------
and the eighth decile.
Locator: 0.80*30 = 24
Round up to 25
80%ile = 54
---------------------------
(b) Determine the 67th percentile.
Locator: 0.67^30 = 20.1
Round up to 22
67%ile = 48
==================
Cheers,
Stan H.
=============

Question 569959: Suppose the Internal Revenue Service is studying the category of charitable contributions. A sample of 32 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 32 returns 7 had charitable contributions of more than $1,000. Suppose 6 of these returns are selected for a comprehensive audit.
(a)What is the probability exactly one of the six audited had a charitable deduction of more than $1,000?
(b)What is the probability at least one of the audited returns had a charitable contribution of more than $1,000?
Answer by stanbon(48510)   (Show Source):
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A sample of 32 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 32 returns 7 had charitable contributions of more than $1,000.
p-hat = 7/32
---------------------------
Suppose 6 of these returns are selected for a comprehensive audit.
(a)What is the probability exactly one of the six audited had a charitable deduction of more than $1,000?
Binomial with n = 6 and p(had) = 7/32 ; p(not had) = 25/32
---
P(x = 1) = 6C1(7/32)(25/32)^5 = binompdf(6,7/32,1) = 0.3820
-------------------------------------------------------------
(b)What is the probability at least one of the audited returns had a charitable contribution of more than $1,000?
P(at least one) = 1 - P(none)
= 1 - (5/32)^6
---
= 1 - 0.0000146
---
= 0.9999
=====================
Cheers,
Stan H.

Question 569969: a test has 2 questions with 5 multiple choice answers per questions. Only 1 answer is correct. What is the probability if answering both questions correct if you guess.
Answer by jim_thompson5910(21667)   (Show Source):
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One answer is correct, so we can ignore that question. So this means that the probability is simply 1/5 = 0.2, which is 20%

Question 569759: dwayne forgot his 4 digit pin number for his bank account. he knows that all four digits are different, and that the two middle numbers are 6 and 8
Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
dwayne forgot his 4 digit pin number for his bank account. he knows that all four digits are different, and that the two middle numbers are 6 and 8
---------
Sorry to hear that.

Question 569722: Suppose a consonant of the alphabet is chosen at random and removed. Then a different consonant is chosen. Are the events in the experiment dependent or independent?

Answer by AnlytcPhil(1116)   (Show Source):
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DEPENDENT because what letters are available to pick second DEPENDS on what was picked first. For instance, if you picked R first, then the second event is AFFECTED because R is not available to be picked for the second event. [Note: If the R were replaced after picking it the first time, then the events would be independent, because what was picked the first time would have no effect on what was picked the second time, but since it isn't replaced, the second event DEPENDS on what was picked the first time.] Edwin

Question 569692: another friends ask you to explain how to tell if two events are dependent or independent ? how would you reply?
Answer by JBarnum(1826)   (Show Source):
You can put this solution on YOUR website!
Dependent and Independent Events
The occurrence of some events may affect the probability of occurrence of others. For example, the complementary events A and A cannot occur simultaneously. If one took place the other is out of the game:
P(A|A) = 0
regardless of the probability P(A). (P(A|B) denotes the conditional probability of A assuming B.) We say that the event A is not independent of the event A (assuming P(A) ≠ 0 of couse.) And, in general, an event A is not independent of an event B iff P(A) ≠ P(A|B), i.e., if occurrence of B affects the probability of A. It may not be obvious right away, but the relationship "not independent" is symmetric: if A is not independent of B then also B is not independent of A. Formally,
if P(A) ≠ P(A|B) then P(B) ≠ P(B|A).
To see why that is so we invoke the defintion of conditional probability,
P(A|B) = P(A∩B) / P(B),
so that P(A) = P(A|B) implies P(A∩B) / P(B) = P(A), or
P(A∩B) = P(A) P(B),
which also may serve as the definition of independency of A from B. But the later relationship is symmetric! It implies
P(B) = P(A∩B)/P(A) = P(B|A),
which exactly means that B is independent of A. We see that two events A and B are either both dependent or independent one from the other. The symmetric definition of independency is this
(*) P(A∩B) = P(A) P(B).
Two events A and B are independent iff that condition holds. They are dependent otherwise.
It's a frequent misconception that the independency or dependency of two events relates to their having or not having an empty intersection. The case of A and its complement A supplies a clear example of two dependent events with empty intersection.
Another example was introduced in the discussion of conditional probabilities, where we considered the sets
Ω = {1, 2, 3, 4, 5, 6, 7, 8},
A = {1, 3, 5, 7},
B = {7, 8},
A+ = {1, 2, 3, 5, 7} and
A- = {3, 5, 7}.

We found that P(B) = 1/4 whilst
P(B|A+) = 1/5,
P(B|A) = 1/4,
P(B|A-) = 1/3.

What this says is that B and A are independent whereas B is dependent on both A+ and A-. (Note that B∩A+ = B∩A = B∩A- = {7}.)

Returning to the question of survival and life expectancy, AN is the event of a new-born reaching the age of N years. By the meaning of it, for N > M, AN⊂AM and therefore AN∩AM = AN. In particular this means that
P(AN∩AM) = P(AN)
so that P(AN∩AM) = P(AN)·P(AM) is equivalent to P(AN) = P(AN)·P(AM) which is only possible if P(AN) = 0 or P(AM) = 1. Since the latter is unrealistic and the former is unlikely for a reasonable age N, the two events AN and AM can't be independent. In fact, the probability of reaching a certain age grows with aging. As the time goes by, the size of the surviving population goes down while the number of person in a certain (advanced) age group is fixed. Thus the probability (which is the ratio of the two quantities) of getting into that group is indeed increasing with age.
in reference to: http://www.cut-the-knot.org/Probability/IndependentEvents.shtml

Question 569652: 3 cards are drawn from 12 face cards of ordinary deck of 52 playing cards. Let x be the number of kings and y be the number of jacks. Find the joint probability distribution of x and y.

Answer by AnlytcPhil(1116)   (Show Source):
You can put this solution on YOUR website!
3 cards are drawn from 12 face cards of ordinary deck of 52 playing cards. Let x be the number of kings and y be the number of jacks. Find the joint probability distribution of x and y.

J♥ Q♥ K♥ J♦ Q♦ K♦ J♠ Q♠ K♠ J♣ Q♣ K♣ The trinomial probability formula for non-negative integers x,y,z where x+y+z = 3 or Let z = the number of queens (i.e., non-jacks, non-kings) Substitution in that formula gives the following trinomial distribution: x y z p(x,y,z) -------------------------------- 0 0 3 1/27 = 0.03703704 0 1 2 3/27 = 0.11111111 = 1/9 0 2 1 3/27 = 0.11111111 = 1/9 0 3 0 1/27 = 0.03703703 1 0 2 3/27 = 0.11111111 = 1/9 1 1 1 6/27 = 0.22222222 = 2/9 1 2 0 3/27 = 0.11111111 = 1/9 2 0 1 3/27 = 0.11111111 = 1/9 2 1 0 3/27 = 0.11111111 = 1/9 3 0 0 1/27 = 0.03703703 Edwin

Question 158200: Scott Equipment Organization is investigating the use of various combinations of short term and long-term debt in financing its assets. Assume that the organization has decided to employ $30 million in current assets, along with $35 in fixed assets, in the operations next year. Given the level of current assets, anticipated sales adn Earnings Before Interest and Taxes (EBIT) for next year are $60 million and $6 million, respectively. The organizations income tax rate is 40%; Stockholders equity will be used to finance $40 million of its assets, with the remainder being financed by short-term and long-term debt. Scott's is considering implementing one of the following financing policies:
Amount of Short-Term Debt
Financial Policy In Mil. LTD% STD%
Aggressive (large amount) $24 8.5 5.5
Moderate (moderate amount) 18 8.0 5.0
Conservative (small amount) 12 7.5 4.5
A) Determine the following for each of the financing policies:
1) Expected rate of return on stockholders equity
2) Net working capital position
3) Current ratio
B) Evaluate the profitability versus risk trade-offs of these three
policies. Would you rate each one "low", "medium", or "high"
with respect to profitability? Would you rate
each "one"low", "medium", or "high" with respect to risk?
Answer by ydscott(1)   (Show Source):
You can put this solution on YOUR website!

Question 569239: What is the probability that the first two letters of a 3 letter license plate are consonants followed by a vowel?
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
What is the probability that the first two letters of a 3 letter license plate are consonants followed by a vowel?
----
# of vowels: 5
# of consonents: 21
-------
Pattern: CCV
# of that pattern: 5*5*21 = 210
---
# of possible patterns: 26^3
----
P(CCV) = 210/26^3 = 0.0119
==================================
Cheers,
Stan H.
======================

Question 569104: Could someone please help me write an equation to describe the exponential function as y=ab^x
The base is 5. The graph passes through the point(1,2)
Thank you for taking the time to help me!
Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
Could someone please help me write an equation to describe the exponential function as y=ab^x
The base is 5. The graph passes through the point(1,2)
--------------

a = 0.4
-->

Question 568992: What is the probability that a yellow marble is drawn at random from a bag containing 3 white, 2 yellow, 1 green, and 4 blue marbles. (Example of how to enter answer: if the answer was two thirds you would enter 2/3)
Answer by htmentor(580)   (Show Source):
You can put this solution on YOUR website!
What is the probability that a yellow marble is drawn at random from a bag containing 3 white, 2 yellow, 1 green, and 4 blue marbles. (Example of how to enter answer: if the answer was two thirds you would enter 2/3)
=======================
There are a total of 10 marbles in the bag, 2 of which are yellow
Therefore the P(yellow) = 2/10 = 1/5

Question 568942: In how many ways can double game of tennis be arranged from eight boys and four girls if each side must have one boy and one girl?
Thanks!
Answer by Theo(2967)   (Show Source):
You can put this solution on YOUR website!
each side must have 1 boy and 1 girl.
this makes the number of possible teams equal to 4 * 8 = 32.
each girl can be paired with any of the 8 boys.

it takes 2 teams to play a game.
the games can be arranged in 32 * 31 / 2 = 496 ways.
32 * 31 / 2 is the combination formula of 32C2.

this would be easier to actually show what happens if there were less boys and girls.

assume there were 2 girls and 3 boys
identify the girls by the letter a and b
identify the boys by the numbers 1 and 2 and 3.
there are 2 * 3 = 6 possible teams.
those teams are
a1
a2
a3
b1
b2
b3
it takes 2 teams to play a game.
the number of possible games where each time plays each other team only once would be given by the formula 6C2 which results in 6 * 5 / 2 which results in 15 possible games.
the possible games to be arranged would be as follows:
-----
a1 plays a2
a1 plays a3
a1 plays b1
a1 plays b2
a1 plays b3
-----
a2 plays a3
a2 plays b1
a2 plays b2
a2 plays b3
-----
a3 plays b1
a3 plays b2
a3 plays b3
-----
b1 plays b2
b1 plays b3
-----
b2 plays b3
-----
the formula can be shown to be applicable with 2 girls and 3 boys.
the same formula is used with 4 girls and 8 boys to get the answer provided above.
number of possible teams if 4 * 8 = 32
number of possible games is 32C2 which is equal to 32 * 31 / 2 = 496.

Question 568882: The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best reate with 80% of its flights arriving on time. A test is conducted by randomly selecting Southwest flights and observing whether they arrive on time.
Find the probability that exactly flights arrive on time
Answer by solver91311(12118)   (Show Source):
You can put this solution on YOUR website!

The probability of successes in trials where is the probability of success on any given trial is given by:

Where is the number of combinations of things taken at a time and is calculated by

Your probability of success on any given trial is given as 80%, but you didn't bother to share the number of trials or the desired number of successes, so you are on your own from here.

John

My calculator said it, I believe it, that settles it

Question 568776: If 4n=3.60, which is the value of the n. Exsamples A.0.09 B.0.9 C.9 D.90.

Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
If 4n=3.60, which is the value of the n. Exsamples A.0.09 B.0.9 C.9 D.90.
-----
4n = 3.6
Divide both sides by 4 to get:
n = 0.9
==============
Cheers,
Stan H.

Question 568857: a bag contains 6 cherry, 3 orange, and 2 lemon candies. you reach in and take 3 pieces of candy at random. whats the probability that you have one candy of each favor.
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
a bag contains 6 cherry, 3 orange, and 2 lemon candies. you reach in and take 3 pieces of candy at random. whats the probability that you have one candy of each favor.
---------------------
# of ways to succeed: 6*3*2 = 36
---
# of random draws of three: 11C3 = 165
----
P(one of each flavor) = 36/165
================
Cheers,
Stan H.

Question 568205: if the correlation between x and y is r= 30 and ssy =100, how much of the y variability is predicted by the regression equation? ss regression = ponts.
a.9
b. 30
c. 70
d. 91
Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
Reread what you typed...r can only be between -1 and 1, not 30.