Question

A firm buys components from two suppliers: 60 percent from supplier A and the rest from supplier B. It so happens that 9 percent of the components from supplier A are defective and 15 percent of the components from supplier B are defective. (a) What is the probability that the next component the firm buys is defective? (b) What is the probability that the component that the firm buys is from supplier B if we know that it is defective?

Answer 1

0.114,0.5263

Explanation:

Given that a firm buys components from two suppliers:

A : 60% Defective 9%

B:40% Defective 15%

a) the probability that the next component the firm buys is defective

=prob purchased from A and defective + prob purchased from B and defective

=
`0.60(0.09)+0.40(0.15)\\= 0.054+0.06\\=0.114`

b) the probability that the component that the firm buys is from supplier B if we know that it is defective

=Prob from B and defective/Prob defective

=
`(0.40(0.15))/(0.114) \\=0.5263`