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 is
a. 11
b.9
c. 7
d. 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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