# Solved (Free): If 5 of a company’s 10 delivery trucks do not meet emission standards and 3 of them are chosen for inspection

#### ByDr. Raju Chaudhari

Mar 13, 2021

If 5 of a company's 10 delivery trucks do not meet emission standards and 3 of them are chosen for inspection, what is the probability that none of the trucks chosen will meet emission standards?

#### Solution

Let $X$ denote the number of trucks that meet emission standard out of 3 trucks.

Let $p$ be the probability that the truck meet emission standards.

Given that $p=5/10 =0.5$ and $n =3$. Thus $X\sim B(3, 0.5)$.

The probability mass function of $X$ is

 \begin{aligned} P(X=x) &= \binom{3}{x} (0.5)^x (1-0.5)^{3-x},\\ &\quad x=0,1,\cdots, 3 \end{aligned}

The probability that none of the trucks chosen will meet emission standards is

 \begin{aligned} P(X= 0) & =\binom{3}{0} (0.5)^{0} (1-0.5)^{3-0}\\ & = 0.125\\ \end{aligned}