You need P(X <= 2) where X is Binomial(5, 0.2).
Model the number of muffin buyers as a binomial random variable with n=5 and p=0.2. The bakery does not run out if at most 2 customers buy muffins, so compute P(X ≤ 2) using the binomial CDF or by summing individual probabilities.
Pro tip: After computing the probability, briefly mention that this is a binomial distribution problem and that the complement (running out) would be P(X ≥ 3). This shows you understand the underlying model and can think about edge cases.
Define X as the number of customers who buy a muffin. Recognize that X follows a binomial distribution with parameters n=5 and p=0.2.
The bakery has only 2 muffins, so it does not run out if X ≤ 2. The event of running out is X ≥ 3.
Calculate P(X ≤ 2) using the binomial formula: sum_{k=0}^{2} C(5,k) * (0.2)^k * (0.8)^{5-k}. Alternatively, use the complement: 1 - P(X ≥ 3).
Perform the arithmetic carefully and state the final probability. Optionally, mention that the expected number of muffin buyers is 1, which is less than 2, so the probability should be high.
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