Question

Assume that a procedure yields a binomial distribution with n=3 trials and a probability of success of p=0.300. use a binomial probability table to find the probability that the number of successes x is exactly 2.

Answer 1

$\mathbb P(X=x)=\begin{cases}\dbinom3xp^x(1-p)^{3-x}&\text{for }0\le x\le3\\\\0&\text{otherwise}\end{cases}$

$\implies\mathbb P(X=2)=\dbinom32(0.3)^2(0.7)^1=0.189=18.9\%$