Answer: n is large and p is small with np = lambda.
- A p is large, close to one, regardless of how large n is
- B n is large and p is small with np = lambda
- C n equals lambda precisely, while p remains otherwise unconstrained
- D p equals 1 over n, with a loose requirement on the size of n
Correct answer: B. n is large and p is small with np = lambda
Explanation: Poisson approximation: as n→∞ and p→0 with np = λ fixed, Binomial(n,p) → Poisson(λ). Rule of thumb: n ≥ 20 and p ≤ 0.05. Models rare events (defects, accidents). P(X=k) = e<sup>−λ</sup>λᵏ/k! replaces C(n,k)pᵏ(1−p)<sup>n−k</sup>.
Venn diagram of the universal set U with events A and B, showing the intersection (A and B), the parts unique to each event, and the complement region outside both.
Concept context
Chance, events, conditional probability, and Bayes theorem