In a factory which manufactures bolts, machines A. B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their outputs, 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and is found to b

Explanation

Let `P(A)=frac{25}{100}, P(B)=frac{35}{100}, P(C)=frac{40}{100}`


`
P(frac{D}{A})=frac{5}{100}, P(frac{D}{B})=frac{4}{100}, P(frac{D}{C})=frac{2}{100}
`


Let `D` is for defective bolts


`P(D)=P(A) cdot P(frac{D}{A})+P(B) cdot P(frac{D}{B})+P(C) cdot P(frac{D}{C})`


`=frac{25}{100} cdot frac{5}{100}+frac{35}{100} cdot frac{4}{100}+frac{40}{100} cdot frac{2}{100}=0.0345`


`P(frac{A}{D})=frac{P(A) cdot P(Z)}{P(A) cdot P(frac{R}{A})+P(B) cdot P(frac{R}{B})+P(C) cdot P(mathbb{Z})}`


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