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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:
2
`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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Knowledge Check

  • A man makes attempts to hit the target. The probabilty of hitting the target is (3)/(5) . Then the probability that a man hits the target exactly 2 times in 5 attempts, is

    A
    `(144)/(625)`
    B
    `(72)/(3125)`
    C
    `(216)/(625)`
    D
    `(32)/(3125)`

  • If the chance of a gushot hitting a target is 0.2 then the probability that at least 2 shots out of 10 will hit the target is

    A
    `1-((4)/(5))^(10)`
    B
    `1-7((4)/(5))^(10)`
    C
    `1+(7)/(2) ((4)/(5))^(10)`
    D
    none of these

  • A rifleman is firing at a distant target and has only 10% chance of hitting it. The number of least rounds, he must fire in order to have more than 50% chance of hitting it at least once is-

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