A rifleman is firing at a distance target and hence has only 10% chance of hitting it. Find the number of rounds; he must fire in order to have more than 50% chance of hitting it at least once.

Options

A. 11
B. 9
C. 7
D. 5

Answer

C

Explanation

Let p be the probability that the rifleman hits the target.
Then,`p=(10)/(100)=(1)/(10)and q =(9)/(10)`
Suppose n rounds are fired. Let X be the number of times the rifleman hits the target in n trials. Then,
`P(X=r)=.^nC_r((1)/(10))^r((9)/(10))^n-r,r=0,1,2,....n`
Now,
`P(X=ge1)ge (1)/(2)`
`rArr 1-P(X=0)ge(1)/(2)`
`rArr P(X=0)lt(1)/(2)rArr ((9)/(10))^n le (1)/(2)rArr n=7,8,9.......`