A problem in Mathematics is given to three students  A, B, C and their respective probability of solving  the problem are 12,13 and 14. Probability that the problem is solved, is 

A problem in Mathematics is given to three students  A, B, C and their respective probability of solving  the problem are 12,13 and 14. Probability that the problem is solved, is 

  1. A

    34

  2. B

    12

  3. C

    23

  4. D

    13

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    Solution:

    Consider the following events: 

    E = Student A solves the problem 

    F = Student B solves the problem 

    G = Student C solves the problem 

    Clearly, E,F,G are independent events such that

    P(E)=12,P(F)=13 and P(G)=14

    Required probability  =P(EFG)

    Required probability = 1P(E¯)P(F¯)P(G¯)

    Required probability = =112×23×34=34

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