Question

A box contains $100$ bolts and $50$ nuts. It is given that $50\%$ bolts and $50\%$ nuts are rusted. Two objects are selected from the box at random. Find the probability that either both are bolts or both are rusted.

• A. $0.44$
• B. $0.58$
• C. $0.52$
• D. $0.48$

Answer 1

Answer: (B)

$0.58$

Answer 2

Total number of objects $= (100 + 50) = 150$. Let $S$ be the sample space. Then, $n(S) =$ number of ways of selecting $2$ objects out of $150$ $= \,^{150}C_{2}$. Number of rusted objects $= (50\%$ of $100) + (50\%$ of $50) = 50 + 25 = 75$.