Question

Please help me solve the following problem. please write neatly.

Sixty 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) P[all of the next three vehicles inspected pass) (b) P(at least one of the next three inspected fails) (c) Pexactly one of the next three inspected passes) (d) Pat most one of the next three vehicles inspected passes) (e) Given that at least one of the next three vehicles passes Inspection, what is the probability that all three pass (a conditional probability)? (Round your answer to three decimal places.)

Answer 1

Criven Let tu probabi lity vandon vechie pases Huat o60 1ep Lest Yandon Variabe be X Can be defin a4 Binonial ditvhution 3-X t/20,2,3 P(x-x) 0.6(-06 P(X- (o-6 (03)3-3 O.216 tee vechile Oof nent find ob5ect one dals So of tu next three inpictd P(Akart one fails)- 1-p(x-3) elo216 of nex t thee insperted pay one 3-1 Cs)oa) (016) 0 336 17

dTo find atmort One od nent three paun Plx PlX-) Plxe) O700.064) (3) (o.6)(0.16) 1 O064 0 288 2 all three nexit three veeutey pauy atteat of par that Plx-31x 2) Plx-3nx21) Plx1) P(x-3) Plx21) 0 216 120.064 o 216 0936 0.230.