If the probability of hitting a target by a shooter,  in any shot, is 1/3, then the minimum number of independent shots at the target required by him so that the probability of hitting the target al least once is greater than 5/6, is

If the probability of hitting a target by a shooter,  in any shot, is 1/3, then the minimum number of independent shots at the target required by him so that the probability of hitting the target al least once is greater than 5/6, is

  1. A

    5

  2. B

    6

  3. C

    3

  4. D

    4

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    Solution:

    Given,p=13, so q=113=23

    Let n be the minimum number of shots required. As per given condition, we have

    1nC0(p)0(q)n>561113023n>5616>23n

     p.1666>23n, which is possible only when we take

    n = 5, 6, ...

      Minimum value of n=5

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