You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is A. 1/4 B. 1/3 C. 1/2 D. 2/3

GATE 2014 · General Aptitude · Conditional Probability · medium

Answer: P(other face = T | top = H) = 1/3

1. Define the face-level sample space: Label the 6 faces: (HH-f1, HH-f2, TT-f1, TT-f2, HT-H, HT-T). Each face is equally likely to be on top when a random coin is tossed: probability 1/6 each.
2. Filter to cases where the top face shows H: Head-showing faces: {HH-f1, HH-f2, HT-H} — exactly 3 out of 6 faces. Each equally likely.
3. Count cases where the OTHER face is tails: Among {HH-f1, HH-f2, HT-H}, only HT-H has tails on the other face. So P = 1/3.