Find The Probability of The Problem will be Solved :

A problem in statistics is given to there students A, B and C whose chances of solving it independently are 1/2 , 1/3 and ¼  respectively. The probability that the problem will be solved is

  1. 1/12
  2. 11/12
  3. 1/2
  4. 3/4
Anurag Mishra Professor Asked on 4th October 2015 in Maths.
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    Answer: (4) 3/4

    Explanation:-

    Let A, B, C be the respective events of solving problem and a, b, c be the respective events of not solving the problem. Then A, B, C are independent events.

    Therefore, a, b, c are independent events

    Then, P (A) = 1/2, P (B) = 1/3 and P (C) = 1/4
    and P (a) = 1/2, P (b) = 2/3  and P (c) = 3/4

    Therefore, P (none solve the problem) = P (not A) and (not B) and (not C)

    = P (a∩b ∩c)
    = P (a) P (b) P (c)
    = 1 x 2 x 3 /2 x 3 x 4
    =1/4
    Then, P (the solve the problem) = 1 – 1/4
    = (4 – 1)/4
    = 3/4

    Hence, the answer is (4) 3/4

    Anurag Mishra Professor Answered on 4th October 2015.
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