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

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Solution

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Official answer: A) 1/3

Probability and Statistics

When two fair coins are tossed, the sample space is:

S = \{HH, HT, TH, TT\}

Let $A$ be the event that both coins show heads:

A = \{HH\}

Let $B$ be the event that at least one outcome is a head:

B = \{HH, HT, TH\}

We need to find the conditional probability $P(A \mid B)$ :

P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{|A \cap B|}{|B|}

Since $A \cap B = \{HH\}$ , we have:

P(A \mid B) = \frac{1}{3}

Hence, the correct option is (A).

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This Probability and Statistics previous year question is Q3 of the GATE CSE 2011 paper. Find more GATE CSE PYQs on Probability and Statistics in Engineering Mathematics, or browse all GATE CSE PYQs.

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