For a Binomial distribution B(n, p), the probability of exactly r succ…

Question

For a Binomial distribution B(n, p), the probability of exactly r successes is

Accepted Answer

B. {'text': 'C(n, r) × pʳ × q^(n−r)', 'label': 'B'}

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: NCERT Class 12 Mathematics, Ch 13 "Probability", §13.7_

Answer

{'text': 'A simple product p × q of success and failure', 'label': 'A'}

Answer

{'text': 'The product n × p × q of trials × p × q', 'label': 'C'}

Answer

{'text': '1 / n regardless of the value of r or p', 'label': 'D'}