The probability of a man hitting a target is 2 5 . He fires at the target k times (k , a given number). Then the minimum k , so that the probability of hitting the target at least once is more than 7 10 , is :

Step-by-step solution

aligned & 2 5 + 3 5 2 5 + ( 3 5 )^2 2 5 + + ( 3 5 )^k 2 5 > 7 10 & 2 5 [1+ 3 5 + ( 3 5 )^2+ + ( 3 5 )^k ]> 7 10 & 2 5 1- ( 3 5 )^k 1- 3 5 > 7 10 1- ( 3 5 )^k> 7 10 & ( 3 5 )^k < 3 10 k 3 aligned Hence minimum value of k=3