Seventy percent of all vehicles examined at a certain emissions inspection stati

Question

Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive vehicles pass or fail independently of one another, calculate the following probabilities. (Enter your answers to three decimal places.) (a) Prall of the next three vehicles inspected pass) (b) at least one of the next three inspected fails) (c) P(exactly one of the next three inspected passes) (d) P(at most one of the next three vehicles inspected passes) (e) Given that at least one of the next three vehicies passes inspection, what is the probability that all three pass (a conditional probablty)? (Round your answer to three decimal places.)

Explanation / Answer

a) P(All three pass) = 0.703 = 0.343

b) P(At least one fail) = 1 - P(All three pass) = 1 - 0.343 = 0.657

c) P(Exactly one pass) = 3*0.7*0.32 = 0.189

d) P(At most one pass) = P(0 pass) + P(1 pass) = 0.33 + 3*0.7*0.32 = 0.216

e) P(All three pass|At least one passes) = 0.73/(1 - 0.33) = 0.353

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