Two fair coins are flipped simultaneously. If event A is 'getting at least one head' and event B is 'getting exactly two heads', what is the conditional probability P(B | A)?
Answer and explanation
Correct answer: C. 1/3
The sample space of two fair coin flips is S = {HH, HT, TH, TT} (4 equally likely outcomes). Event A (at least one head) = {HH, HT, TH}, so P(A) = 3/4. Event B (two heads) = {HH}, which is a subset of A, so A intersect B = {HH} with P(A intersect B) = 1/4. By conditional probability: P(B | A) = P(A intersect B) / P(A) = (1/4) / (3/4) = 1/3.
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