Home › MHT-CET › Mathematics › Binomial Distribution › If $X \sim B(n, p)$, the probability of exactly …
If $X \sim B(n, p)$, the probability of exactly $x$ successes is:
A${}^nC_x p^x q^{n-x}$ where $q = 1 - p$
B$n \cdot p^x \cdot q^{n-x}$
C${}^nC_x p q$
D$(p + q)^n$
Answer & 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 $(q + p)^n$.
Related questions
A multiple-choice exam has 10 questions each with 5 options. The probability that a studenA bulb-factory has 5% defectives. In a random sample of 10 bulbs, the probability of **notIn a 5-trial binomial distribution, $P(X = 1) = 0.4096$ and $P(X = 2) = 0.2048$. The probaIf success probability in a single trial is 0.01, the minimum number of trials needed so tProbability of bomb hitting target = 0.8. Out of 10 bombs dropped, probability that **exacIf $X im B(4, p)$ and $P(X = 0) = 16/81$, then $P(X = 4)$ equals:Mean and variance of a binomial distribution are 18 and 12 respectively. The value of $n$ The probability that a shooter hits a target is 3/4. The minimum number of shots required