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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 is a. 11 b.9 c. 7 d. 5

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

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

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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Badiuddin

                   

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