A man who goes to work long before sunrise every morning gets dressed in the…
2026
A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer he has 6 black socks and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?
- A.
24/91
- B.
1/24
- C.
1/7
- D.
13/48
Attempted by 1 students.
Show answer & explanation
Correct answer: A
When two events happen in sequence without replacement, the combined probability is the product of the first event's probability and the second event's probability conditioned on the first having occurred: P(first, then second) = P(first) × P(second | first), where the second probability is computed over the reduced pool of items left after the first draw.
Applying this to the sock drawer:
The drawer holds 6 black socks and 8 blue socks — 14 socks in total.
Probability the first sock drawn is black: 6/14.
Once a black sock is removed, 13 socks remain (5 black, 8 blue). Probability the second sock drawn is blue, given the first was black: 8/13.
Multiply the two probabilities: (6/14) × (8/13) = 48/182 = 24/91.
Cross-check using counting: the number of ordered ways to draw black-then-blue is 6 × 8 = 48, and the total number of ordered ways to draw any 2 socks from 14 is 14 × 13 = 182, giving 48/182 = 24/91 — the same result.