Answer to Question #206095 in Statistics and Probability for Richa

Question #206095

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?


1
Expert's answer
2021-06-14T14:09:56-0400

Let D represent defective.

P(BD)=P(DB)P(B)P(DB)P(B)+P(DA)P(A)P(B|D)=\frac{P(D|B)P(B)}{P(D|B)P(B)+P(D|A)P(A)}

=125×57(125×57)+(120×27)=23=\frac{\frac{1}{25}×\frac{5}{7}}{(\frac{1}{25}×\frac{5}{7})+(\frac{1}{20}×\frac{2}{7})}=\frac{2}{3}



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