Question

A large shipment of batteries consists of three brands, say A, B, and, C. One battery of each brand will be randomly selected and tested to determine if they work properly. Assume that whether one battery works properly or not is independent of any other battery working properly or not. Let WA=brand A works properly WB=brand B works properly WC=brand C works properly Assume we know that the probabilities of the brands working properly are given by: P(WA)=.90 P(WB)=.85 P(WC)=.95 Find the probability that brand B does not work properly and find the probability that all three randomly selected batteries work properly and find the probability that brand A does not work properly. Based on the information given, when determining P(WA) a valid method of assignment is given. Find the probability that all three randomly selected batteries work properly. That is, the probability that brand A works and brand B works and brand C works. Find the probability that none of the three randomly selected batteries work properly.

Answer 1

Probability that brand B does not work properly = 1 - P(WB) = 1 - 0.85 = 0.15

Probability that all three randomly selected batteries work properly = P(WA WB WC)

= P(WA) P(WB) PWC) (All are independent events)

= 0.90 * 0.85 * 0.95

= 0.72675

Probability that brand A does not work properly = 1 - P(WA) = 1 - 0.90 = 0.10

Probability that none of the three randomly selected batteries work properly = (1 - P(WA)) (1 - P(WB)) (1 - P(WC))

= (1 - 0.90) * (1 - 0.85) * (1 - 0.95)

= 0.00075