Official PYQ · 2004Q25Probability: Random Variables and DistributionsMCQ1 mark

GATE CS 2004 Q25 — Probability: Random Variables and Distributions

If a fair coin is tossed four times. What is the probability that two heads and two tails will result?

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Answer: A

When a fair coin is tossed $4$ times, the total number of possible outcomes is $2^4 = 16$ .

We want to find the probability of getting exactly two heads (and consequently, two tails). The number of favorable outcomes is the number of ways to choose $2$ positions for the heads out of the $4$ tosses:

\binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6

Thus, the required probability is:

P(\text{2 Heads and 2 Tails}) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{6}{16} = \frac{3}{8}

Hence, the correct option is A.

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Published 10 Oct 2026

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