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

(a)
`p(x= 0)=9.536* 10^(-7)` (b) p(x> 1)=0.999

Step-by-step explanation:

Probability that sharpshooter hit the target
`p=0.75=(3)/(4)`

We know that
`p+q=1`

So
`q=1-p=1-(3)/(4)=(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(1)/(4)^(10)`

`=9.536* 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(1)/(4)^(10)`

`p(x> 1)=0.999`