(10 points) Of the microprocessors manufactured by a certain process, 7% are def

Question

(10 points) Of the microprocessors manufactured by a certain process, 7% are defective. Five microprocessors are chosen at random. Assume they function independently. 1, a. What is the probability that all 5 microprocessors work? 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 p at least one test is positive if the athlete was using steroids? robability 0.81 of being positive if steroids have been used. What is the probability that

Explanation / Answer

1)

a) due to independence ; with multiplicative property:

probability that all 5 microprocessor works =(1-0.07)5 =0.6957

b) P(at least one of 5 microporcessor work) =1-P(all 5 are defective)=1-(0.07)5 =1-0.000002 =0.999998

2)

P(at least one test is positive) =1-P(both test are negative) =1-(1-0.72)*(1-0.81)=0.9468

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