GATE2015-2-5

Question

Three vendors were asked to supply a very high precision component. The respective probabilities of their meeting the strict design specifications are $0.8$, $0.7$ and $0.5$. Each vendor supplies one component. The probability that out of total three components supplied by the vendors, at least one will meet the design specification is ___________

Answer 1

P(atleast one) = 1 – P(none)

P(1^st vendor not satisfying) = 1 – 0.8) =0.2

P(2nd vendor not satisfying) = 1 – 0.7) =0.3

P(3rd vendor not satisfying) = 1 – 0.5) =0.5

Therefore, P(none) = 0.2*0.3*0.5 = 0.03

Hence ans = 1 – 0.03 = 0.97