a O points Devasts 2E SE7 Seventy percent of all vehides examined at a certain e

Question

a O points Devasts 2E SE7 Seventy percent of all vehides examined at a certain emissions inspection station pass the inspection. Acauming that successive vehicles pass or fail independently of one another, calculate the following probabilities. (Enter your answers to three decimal places, (a) Pall of the next three vehicles inspected pass (b) A at least one of the next three inspected fails) (c) Pexactly one of the next three inspected passes) (8) A at most one of the next three vehicles inspected passes) (e) Given that at least of the next three vehicles one passes inspection, that all three pass (a conditional probability) (Round your answer to three decimal places.) what is the probability Lauren has that Sue Roonents are eagement he is wome My agents take an importal

Explanation / Answer

p=0.7 (or 70%) thus q=probability of fail=1-0.7=0.3

a) P(all pass)=p3=(0.7)^3=0.343

b) P(atleast 1 fails)=1-P(all pass)=1-0.343=0.657

c) P(exactly one passes)=P(one passes and other two fail)= 3C1*(0.7)*(0.3)^2 = 3*(0.7)*(0.3)^2 =0.189

d) P(atmost one passes)= P(none passes)+P(exactly one passes)= 0.3^3 + 0.189 =0.216

e) P(atleast one passes)=1-P(none pass)=1-(0.3)^3=0.973

P(all 3 pass | atleast 1 passes) =P(all 3 pass and atleast 1 passes)/P(atleast 1 passes)=P(all 3 pass)/P(atleast 1 passes)= 0.343/0.973 =0.3525

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