Question

A company has two plants to manufacture bicycles. Plant I manufactures 70% of the bicycles and plant II manufactures 30%. At plant I 80% of the bicycles are rated as of standard quality and a plant II 90% of the bicycles are rated as of standard quality. A bicycle is choosen at random and is found to be of standard quality. What is the probability that it has come from plant II?

Answer 1

Answer : 27 / 83

Guide :

Assume the following

A : Event that bicycle is of standard quality

E1 : Bicycle chosen is from Plant 1

E2 : Bicycle chosen is from Plant 2

P(E2|A) = P(A|E2) x P(E2) + P(A|E1) x P(E1)

$\frac{P(A|E2) \times P(E2)}{P(A|E2) \times P(E2) + P(A|E1) \times P(E1)}$

Put :

P(A|E1) = 8/10

P(A|E2) = 9/10

P(E1) = 7/10

P(E2) = 3/10

You will get the answer.

Hope this helps !!!