Question

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. A. 11 B. 9 C. 7 D. 5 Select the correct answer from above options

Answer 1

Correct Answer - C 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.......`