Question

two factories produce similar ammeters. firm a produces 1000 ammeter out of which 50 are defective. firm b produces 2500 ammeters out of which 100 are defective. what is the probability that an ammeter chosen at random and found to be defective belongs to firm b?

Answer 1

Let D represent defective.

$P(B|D)=\frac{P(D|B)P(B)}{P(D|B)P(B)+P(D|A)P(A)}$

$=\frac{\frac{1}{25}×\frac{5}{7}}{(\frac{1}{25}×\frac{5}{7})+(\frac{1}{20}×\frac{2}{7})}=\frac{2}{3}$