Question

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X=14), n=15, p=0.8

Answer 1

Use the PMF for the given distribution:

$P(X=x) = \begin{cases}\dbinom{15}x 0.8^x (1-0.8)^{15-x} & \text{if } x \in\{0, 1, 2, \ldots, 15\} \\ 0 & \text{otherwise}\end{cases}$

Then the probability that X = 14 is

$P(X=14) = \dbinom{15}{14} 0.8^{14} 0.2^1 \approx \boxed{0.1319}$