NDA 2019 Maths · Mathematics · Probability · hard

Machines A and B produce 60% and 40% of the items in a factory, and 2% and 5% of their output respectively is defective. An item picked at random is…

Single correct option

Machines

A

and

B

produce

60\%

and

40\%

of the items in a factory, and

2\%

and

5\%

of their output respectively is defective. An item picked at random is found defective. The probability that it was produced by

B

Show answer and solution

Answer: (A) $\frac58$

By Bayes' theorem,

P(B\mid D)=\frac{0.4\times0.05}{0.6\times0.02+0.4\times0.05}=\frac{0.020}{0.032}=\frac58

. The value

0.05

(or

\frac{1}{20}

) is merely the defective rate of

B

, and

\frac38

is the probability of

A

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake