If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads? A. 1/3 B. 1/4 C. 1/2 D. 2/3

GATE 2011 · Engineering Mathematics · Conditional Probability · easy

Answer: P(both heads | at least one head) = 1/3. Answer: A.

1. Identify event B (at least one head): P(B) = P(at least one head) = 1 - P(TT) = 1 - (1/2)*(1/2) = 1 - 1/4 = 3/4.
2. Find P(both heads and at least one head): Both heads (HH) automatically satisfies at least one head, so A is a subset of B. P(A and B) = P(HH) = 1/4.
3. Apply conditional probability formula: P(both heads | at least one head) = (1/4) / (3/4) = 1/3.