Answer to Question #168004 in Statistics and Probability for DAN

Question

The probability of a man hitting a target is 1/4. He fires 6 times. Find the probability that he hits the target at least once.

Answer 1

We have that

P(hitting a target) = 1/4 = 0.25

n = 6

Need to find $P(X\ge1) = 1-P(X=0)$

This follows binomial distribution.

The binomial probability is calculated by the formula:

$$P(X=m)=C(n,m)\cdot p^m \cdot (1-p)^{n-m}$$

where m = 0

$P(X=0)=C(6,0)\cdot 0.25^0 \cdot (1-0.25)^{6-0}=\frac{6!}{0!6!}\cdot0.25^0\cdot0.75^{6}=0.178$

$P(X\ge1) = 1-P(X=0)=1-0.178=0.822$

Answer: 0.822