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Vaibhav Mathur Grade: 12
        

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

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

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


                   

7 years ago
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