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A shooter can hit a given target with pr...

A shooter can hit a given target with probability `(1)/(4)`. She keeps firing a bullet at the target until she hits ig successfully three times and then she stops firing. The probability that she fires exactly six bullets lies in the interval .

A

(0.5272,0.5274)

B

(0.2636,0.2638)

C

(0.1317,0.1319)

D

(0.0658,0.0660)

Text Solution

Verified by Experts

The correct Answer is:
D
`3^(rd)` time target will hit in sixth time
So, In first 5 attempt these will be 3L,2W and at `6^(th)` attempt shot will be hit
So,
`""^(5)C_(3)((3)/(4))^(3)xx((1)/(4))^(2)xx((1)/(4))=(270)/(4096)=0.06591`
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