Question

The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 2 will miss the target.

Answer 1

This problem represents a binomial experiment with a total of 10 trials. There are 8 successes with the probability of success being 0.8. There are two failures with the probability of failure being 0.2.

The formula to calculate the probability of of $k$ out of $k$ success, with success probability $u$ is,

$P(k)=\left[\begin{array}{cc}n\\k\\\end{array}\right] u^k(1-u)^{n-k}\\\\P(8)=\left[\begin{array}{cc}10\\8\\\end{array}\right] (0.8)^8(1-0.8)^{8-2}=0.302$