A shooter can hit a given target with probability 1/4.she keeps firing a bullet at the target until she hit it successfully three times and then she stops firing . the probability that she fires exactly six bullets is ?
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First the total no of cases is 6!/3!3! (Since there is only 2 outcomes ,hit or miss,and they are in equal proportion ,3 times,by the question). Now the no of favourable outcomes is5!/ 2!3!(since the last fire is confirmed hit.
The answer getting is 1/2 for thee above method. When you multiply it by the probability of hitting you get 0.165 .
I'm not sure about the step may be this get you the closest range.
By your clue of range the only answer possible is 0.0659 since it is the only term b/w the given range.
The answer lies in the interval (0.0658,0.0660)