Question

1) Three dice are rolled. If each lands on a different number, find the probability that one is 3?

2) ) Three machines (A, B, C) manufacture screws. They manufacture 25%, 35%, and 40% of the screws, respectively. The output screws are defective at 2%, 3%, and 5%, respectively. If you choose a random screw produced at the factory and it is defective, what is the probability it came from each machine A, B, and C

Answer 1

1) Probability of a 3 on one die = 1/6

Probability of not 3 on one die = 5/6

Probability of one 3 on three roll of dice = 3*(1/6* 5/6 *5/6) = 0.3472

2) P(A) = 0.25, P(B) = 0.35, P(C) = 0.40

Probability that the screw is defective given that it is from A, P(D|A) = 0.02

Probability that the screw is defective given that it is from B, P(D|B) = 0.03

Probability that the screw is defective given that it is from C, P(D|C) = 0.05

i) Probability that the screw is from A given that it is defective, P(A|D) =

ii) Probability that the screw is from B given that it is defective, P(B|D) =

iii) Probability that the screw is from C given that it is defective, P(C|D) =