Question

A fireman is firing at a distant target and has only 10% chance of hitting it. the number of rounds, he must fire in order to have 50% chance of hitting it at least once is

Answer 1

let he fire n number of times.
so he will miss (n-1) times and at nth time he will hit
total probability
= 1/10 + 9/10 *1/10 + 9/10 *9/10 *1/10 + .....(9/10) n-1 *1/10 = 50/100
=1/10[ 1+ (9/10) + (9/10) 2 + ............(9/10) n-1 ] =5/10
or [1- (9/10) n ]/(1-9/10) =5
0r 1-(9/10) n =1/2 (9/10) n =1/2 nlog9/10 = log1/2
n = log.5 / log.9 =6.58
so he must hit at least 7 times