A family has two children.
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A family has two children. Find the probability that both the children are girls given that at least one of them is a girl?
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Answer: C. C) 1/3
The sample space of 2 children is {BB, BG, GB, GG}. Given at least one is a girl leaves {BG, GB, GG} (3 outcomes). The event that both are girls is {GG} (1 outcome), giving probability 1/3.
Step-by-step Derivation:
Step 1: Sample space S = {BB, BG, GB, GG}, each with probability 1/4.
Step 2: Condition event A (at least one girl) = {BG, GB, GG} with |A| = 3.
Step 3: Target event B (both girls) = {GG} with |A intersect B| = 1.
Step 4: P(both girls | at least one girl) = 1 / 3.