Question 112034: It is known that 10% of all people are left handed. A sample of 10 students is selected at random. What is the probability that 2 of these 10 students is left handed? Find the probability that none of the students are left handed?
Here are my thought:
The events are mutually exclusive and follow normal distibution. If you have a sample size of ten and take the only left handed person out of the sample on the first selection, then there is zero probability that there are any remaining left handed people. The converse applies the the second part of the question.
So my answers are zero for the probability that two are left handed and zero for the probability that none are left handed.
Thanks for you help.
Cheers
CC
Answer by Edwin McCravy(20059)   (Show Source):
You can put this solution on YOUR website! It is known that 10% of all people are left handed. A sample of 10 students is selected at random. What is the probability that 2 of these 10 students is left handed? Find the probability that none of the students are left handed?
No, I'm afraid you're off the track. These are BINOMIAL problems!
You can use any of these three methods:
Method 1. Calculate it by the formula:
P(exactly x out of n) =  
where n = the number of trials = 10
p = the probability of selecting one lefty in one trial, 10% or .1
x = the number you want to find the probability of getting,
which is 2 in the first problem and 0 in the second.
P(exactly 2 out of 10) =  
P(exactly 2 out of 10) =  
P(exactly 2 out of 10) =  
P(exactly 2 out of 10) = 
For the second problem:
P(exactly 0 out of 10) =  
P(exactly 0 out of 10) =  
P(exactly 0 out of 10) =  
P(exactly 0 out of 10) = 
==============================================================
Method 2. Look it up in the binomial probability table in the
back of your book.
1. Find the section of that table that reads n = 10.
2. Read across until you come to p = 0.1
3. Run your finger down that column until to see 2 on the far left
of your finger.
A. If you read .1937 then that's the answer, for you have an "exact
value" table.
B. If you read .9298 then you have a "cumulative value" table, so
1. Find the number directly above that one in the table, which will
have 1 at the far left, and read .7361.
2. Subtract .9298 - .7361 and get .1937
For the second problem
1. Find the section of that table that reads n = 10.
2. Read across until you come to p = 0.1
3. Run your finger down that column until to see 0 on the far left
of your finger, and read .3487. (That should be the very first
entry in that column)
(Note: it makes no difference which kind of table you have
for 0, since there is no cumulation for 0)
===================================================================
Method 3. TI-83 or 84 graphing calculator
For your first problem:
1. Press 2nd VARS ALPHA MATH
You should see this on your screen: binompdf(
2. Type in 10,.1,2) so that you see this: binompdf(10,.1,2)
3. Press ENTER and read .1937102445
For your second problem:
1. Press 2nd VARS ALPHA MATH
You should see this on your screen: binompdf(
2. Type in 10,.1,0) so that you see this: binompdf(10,.1,0)
3. Press ENTER and read .3486784401
Edwin
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