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A man firing at a distant target has 10% chance of hitting the taget in one shot.The number of times he must fire at the target to have about 50%chance of hitting the target isa. 11b.9c. 7d. 5
Dear Vaibhav
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
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