Question

A sharpshooter can hit the target with a probability p=0.75. a) What is the probability that out of 10 shots she misses them all? b) Find the probability that out of 10 shots she gets the target at least once.

Answer 1

Answer:

(a) $p(x= 0)=9.536\times 10^{-7}$   (b) p(x> 1)=0.999

Explanation:

Probability that sharpshooter hit the target $p=0.75=\frac{3}{4}$

We know that $p+q=1$

So $q=1-p=1-\frac{3}{4}=\frac{1}{4}$

(a) The probability that she misses all the shots

Using binomial theorem $^{n}C_{r}p^rq^{n-r}$

$=^{10}C_{0}p^0\frac{1}{4}^{10}$

$=9.536\times 10^{-7}$

(B) Probability that at least one shot hit the target

$p(x> 1)=1-p(x=0)$

$p(x> 1)=1-^{10}C_{0}p^0\frac{1}{4}^{10}$

$p(x> 1)=0.999$