Question

The chances of defective screws in three boxes A, B and C are $\frac{1}{5},\frac{1}{6},\frac{1}{7}$ respectively. A box is selected at random and a screw drawn from it at random, is found to be defective. The probability that it came from the box 'A' is

• A. $\frac{16}{29}$
• B. $\frac{1}{15}$
• C. $\frac{27}{59}$
• D. $\frac{42}{107}$

Answer 1

Answer: (D)

$\frac{42}{107}$

using Baye's Law,
$P\left(E_A|A\right)=\frac{{}^3{C}_1\times \frac{1}{5}}{{}^3{C}_1\times \frac{1}{5}{+}^3{C}_1\times \frac{1}{6}{+}^3{C}_1\times \frac{1}{7}}=\frac{42}{107}$