Question

The probability that a certain kind of component will survive a check test is $0.6$. Find the probability that exactly $2$ of the next $4$ tested components survive.

Answer 1

Let $p$ be the probability that a certain kind of component will survive a check test.
Then, $p=0.6$
$\therefore q=1-p=1-0.6=0.4$
Given, $n=4$
By binomial distribution
$p(X=r){=}^n{C}_r{p}^r{q}^{n-1},0\le r\le n$
$\therefore$ Probability that exactly $2$ of the next $4$ tested components survive
$=p(X=2)$
${=}^4{C}_2\left(0.6{)}^2\right(0.4{)}^{4-2}$
$=\frac{4!}{2!(4-2)!}\left(.36\right)\left(0.16\right)$
$=6\left(0.36\right)\left(0.16\right)$
$=0.3456$.