For a Poisson random variable, the probability of exactly k events is P(X = k) = e^−λ λ^k / k!, where λ is the mean number of events per interval. Here, λ = 4 and the question asks for exactly 2 events, so k = 2. Substitute into the formula: P(X = 2) = e^−4 × 4² / 2!. Since 4² = 16 and 2! = 2, this becomes e^−4 × 8. Numerically, e^−4 is about 0.0183, and 0.0183 × 8 ≈ 0.1465. Thus, the probability is approximately 0.1465. Options B, C, and D are unsupported by the Poisson probability formula. The Poisson model is appropriate for counts of events occurring independently over a fixed interval at a constant average rate. Study Guide references/topics: Poisson distribution, λ parameter, exact event probability, discrete distributions.

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