1. (10 points) of the microprocessors manufactured by a certain process, 7% are

Question

1. (10 points) of the microprocessors manufactured by a certain process, 7% are defective. Five microprocessors are chosen at random. Assume they function independently. a. What is the probability that all 5 microprocessors wor k? b. What is the probability that at least one of the 5 microprocessors works? 2. (10 points) An athlete suspected of having used steroids is given two tests that operate independently of each other. Test A has probability 0.72 of being positive if steroids have been used. Test B has probability 0.81 of being positive if steroids have been used. What is the probability that at least one test is positive if the athlete was using steroids?

Explanation / Answer

Question 1

a) X: no of microprocessors working

P(X=5) = (5C5)*(0.93)^5

P(X=5) = 0.696

b) P(at least one of the 5 works) = 1-P(No one works)

= 1- (5C5)*(0.07)^5

= 0.999998

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