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A man firing a distant target has 20% ch...

A man firing a distant target has `20%` chance of hitting the target in one shot. If P be the probability of hitting the target in atmost 'n' attempts where `20P^(2)-13P+2 le0`. then maximum value of n is.

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The correct Answer is:
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`20P^(2)-13P+2le0`
`rArr" "(4P-1)(5P-2)le0" "rArr" "(1)/(4)le P le(2)/(5)`
`rArr" "(1)/(4)le(1)/(5)+(1)/(5)((4)/(5))+(1)/(5)((4)/(5))^(2)+…….+(1)/(5)((4)/(5))^(n-1)le(2)/(5) rArr 4le n le 7`
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