alleryFor a Binomial distribution B(n, p), the probability of exactly r successes is
AA simple product p × q of success and failure
BC(n, r) × pʳ × q^(n−r)
CThe product n × p × q of trials × p × q
D1 / n regardless of the value of r or p
Answer & Solution
Correct answer: B. C(n, r) × pʳ × q^(n−r)
1. Binomial PMF gives the probability of exactly r successes in n independent trials.
2. Formula: P(X = r) = C(n, r) × pʳ × q^(n−r), where q = 1 − p.
3. C(n, r) counts the number of ways to arrange r successes among n trials.
4. Mean is n p and variance is n p q.
_Source: syllabus Mathematics, Ch 13 "Probability", §13.7_
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