You are a professional athelete whose league requires randomly selected drug tests. For each drug test 14% of the athletes are selected. What is the probability

Question

You are a professional athlete whose league requires randomly selected drug tests. For each drug test 14% of the athletes are selected. What is the probability that you will be selected once in 5 consecutive random drug tests?

 

A-0.470427

B-0.452992

C-0.999946

D-0.529573

Answer 1

This seems to be a poorly constructed problem since the probability of being selected once is 5(.86)⁴(.14)≈0.382905712. This is the probability of not getting selected 4 times times the probability of getting selected once times the number of combinations which include getting selected once.

Based on the answers that are provided my guess is that the problem means to ask what the probability of getting selected at least once in 5 consecutive random drug tests. This is most easily computed by using the identity P(A)=1 − P(not A) since the probability of not getting selected is (1 − .14)⁵ = .86⁵. So the probability of getting selected at least once is 1 − .86⁵ ≈ 0.5295729824.