# Solved (Free): If the probability of hitting a target on a single shot is 0.3, what is the probability

#### ByDr. Raju Chaudhari

Mar 15, 2021

If the probability of hitting a target on a single shot is 0.3, what is the probability that in 4 shots the target will be hit at least 3 times?

#### Solution

The probability of hitting a target on a single shot is $p = 0.3$. Number of shots targeted is $n=4$.

Let $X$ number of shots hot the target. $X\sim B(4, 0.3)$.

The probability mass function of $X$ is
 \begin{aligned} P(X=x) &= \binom{4}{x} (0.3)^x (1-0.3)^{4-x},\\ &\quad x=0,1,\cdots, 4. \end{aligned}

The probability that it will hit at least 3 times is

 \begin{aligned} P(X\geq 3) &= P(X=3) + P(X=4)\\ & =\binom{4}{3} (0.3)^{3} (1-0.3)^{4-3}+ \binom{4}{4} (0.3)^{4} (1-0.3)^{4-4}\\ &= 0.0756+ 0.0081\\ &= 0.0837 \end{aligned}