<p>A man has 3 pairs of black socks and 2 pairs of brown socks kept together in a box. If he dressed hurriedly in the dark, the probability that after he has put on a black sock, he will then put on another black sock is</p>
Step-by-Step Solution
Key Concept: After drawing one black sock, the remaining composition changes: now there are 5 black socks and 4 brown socks left in the box (treating each sock individually from 3 pairs of black = 6 socks, 2 pairs of brown = 4 socks). Use conditional probability with the reduced sample space.
<p><strong>Step 1:</strong> Count total socks initially. 3 pairs black = 6 black socks; 2 pairs brown = 4 brown socks. Total = 10 socks.</p><p><strong>Step 2:</strong> Given that one black sock has been put on, remove it from the box. Remaining socks: 5 black and 4 brown = 9 socks total.</p><p><strong>Step 3:</strong> Find probability that the next sock drawn is also black from this reduced set.</p><p>P(2nd sock is black | 1st sock is black) = 5/9</p><p>∴ Answer: C (which is 5/9)</p>
Correct Answer: C