alleryStart learning →If $X \sim B(n, p)$, the probability of exactly $x$ successes is:
- ${}^nC_x p^x q^{n-x}$ where $q = 1 - p$
- $n \cdot p^x \cdot q^{n-x}$
- ${}^nC_x p q$
- $(p + q)^n$
Show answer and solution
Correct answer: A. ${}^nC_x p^x q^{n-x}$ where $q = 1 - p$
Binomial p.m.f.: $P(X = x) = {}^nC_x \cdot p^x \cdot q^{n-x}$, where $q = 1 - p$.
This is the $(x+1)^{th}$ term in the binomial expansion of $(q + p)^n$.