1. Four candidates are seeking election to one vacancy on a school board. If can

Question

1. Four candidates are seeking election to one vacancy on a school board. If candidate A is twice as likely to be elected as candidate B, and candidate B and candidate C are equally likely to be elected, while candidate C is twice as likely to be elected as candidate D, what are the probabilities that a. candidate C will be elected? b. candidate A will not be elected? c. candidate D will elected? 2. A weighted tetrahedral (4 faced) die has a probability equal to kj of showing face j, where k is a constant and j - 1, 2, 3, 4 a. Find k and the probability that j > 2. b. Find the expected value of the value of the face showing. c. Find the standard deviation of the value of the face showing. To pass the Texas Ranger marksmanship test, a candidate is required to shoot at a target until he scores a bull's-eye. The candidate is judged on the number of trials that are necessary to achieve this score. Assume the probability of his hitting a bull's-eye on any trial is 0.40 a. Find the probability that the candidate requires exactly 4 shots b. Find the probability that the candidate requires more than 2 but less than 5 shots. 3. c. Find the expected value of number of trials.

Explanation / Answer

Solution

1) given that P(A) = 2P(B)

P(B) = P(C)

P(C) = 2 P(D)

a) P(A) + P(B) + P(C) + P(D) = 1

2P(C) + P(C) + P(C) + 0.5P(C) = 1

P(C) = 2/9

b) P(not A) = 1 - P(A)

P(A) + P(B) + P(C) + P(D) = 1

P(A) + 0.5P(A) + 0.5P(A) + 0.25P(A) = 1

P(A) = 4/9

P(not A) = 5/9

c) P(A) + P(B) + P(C) + P(D) = 1

4P(D) +2P(D) +2P(D) + P(D) = 1

P(D) = 19

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