A man who goes to work long before sunrise every morning gets dressed in the…
2025
A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer he has 6 black 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.
91/24
- B.
25/19
- C.
19/25
- D.
24/91
Attempted by 2 students.
Show answer & explanation
Correct answer: D
When two events happen in sequence without replacement, they are dependent — the outcome of the first event changes the sample space for the second. The joint probability of two dependent events A and B is P(A and B) = P(A) × P(B | A), where P(B | A) is computed using the reduced total after A has occurred.
Total socks in the drawer at the start = 6 black + 8 blue = 14 socks.
Probability the first pick is black: 6 black socks out of 14 total, so P(black first) = 6/14.
After removing one black sock, 13 socks remain (5 black, 8 blue) — the count of blue socks is unchanged at 8. So P(blue second | black first) = 8/13.
Multiply the two dependent probabilities: P(black then blue) = 6/14 × 8/13 = 48/182.
The probability tree below shows both draws and their branch probabilities.
Simplify 48/182 by dividing numerator and denominator by their common factor 2: 48/182 = 24/91. This fraction is already in lowest terms (91 = 7 × 13 shares no factor with 24 = 2³ × 3), confirming the final probability is 24/91.