SOLUTION: Q.1 A biased die is rolled 500 times and the number 6 came up 83 times. a) What is the experimental probability of a 6 occurring? b) What are the odds of the number 6 coming up i

Algebra ->  Probability-and-statistics -> SOLUTION: Q.1 A biased die is rolled 500 times and the number 6 came up 83 times. a) What is the experimental probability of a 6 occurring? b) What are the odds of the number 6 coming up i      Log On


   

Question 1058526: Q.1 A biased die is rolled 500 times and the number 6 came up 83 times.
a) What is the experimental probability of a 6 occurring?
b) What are the odds of the number 6 coming up in this experiment?
c) If the odds that a three will come up 12 times in 72 rolls of a die, what is probability that a three would come up ?
Q.2 Below are 2 boxes with black and white marbles.
BOX 1 HAS 1 BLACK AND 2 WHITE MARBLES
BOX 2 HAS 3 BLACK AND 1 WHITE MARBLES
A box is selected and then a marble is drawn from the
selected box. Draw a tree diagram to and indicate on the diagram where you would find the
probability of selecting black marble given it came from box 2.
Q.3 Determine if each pair of events are dependent or independent.
A. Event A: making a 10 foot putt.
Event B: making another 10 foot putt.
B. Event A: high surf
Event B: windy conditions offshore.
C. Event A: choosing a King from a deck of cards and replacing it.
Event B: then choosing a King.
D. Event A: flipping a coin and landing tails up in British Columbia.
Event B: flipping a coin and landing heads up in Alberta.
Q.4 Determine if each pair of events are mutually exclusive or not mutually exclusive.
A. Event A: selecting a spade from a standard deck of cards.
Event B: selecting a red card from a standard deck of cards.
B. Event A: selecting the queen of clubs from a standard deck of cards.
Event B: selecting a black queen from a standard deck of cards.
C. A pair of dice is rolled.
Event A: the sum of the two dice is 8.
Event B: the two dice are a pair.
D. A pair of dice is rolled.
Event A: the sum of the two dice is 3
Event B: the two dice are a pair.
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
1.a. The expected value is 500/6=83.3
b. The odds appear to be 83.3/416.7=1 in 5. Note that odds and probability are not the same. This is a probability of 0.166
c. If the probability is 12/72 or 1 in 6.
2.
1================================2 Each is 0.5
b---w----w==================b----b----b----w
b is 1/3; w is 2/3--------------------b is 3/4, w is 1/4. This is Q2, p(b) given it came from box 2.
The overall prob of b is 1/6 (from 1) and 3/8 from 2 or 26/48 or 13/24
The overall prob of w is 1/3 from 1 and 1/8 from 2 or 22/48 or 11/24.
3.
Dependent upon knowledge of the green after putting the first time. The two are not exactly under the same circumstances.
Dependent in that windy conditions offshore can produce high surf. The reverse is not true.
Independent. Nothing is different the second time.
Independent. The province does not affect the coin toss.
4. Mutually exclusive. A spade is not a red card.
Not mutually exclusive the QC is a black queen
Not mutually exclusive. 4-4 can make 8.
Mutually exclusive. A pair of dice cannot be the same number and the sum 3.