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Q: A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

  • 1
    1/4
  • 2
    1/2
  • 3
    3/4
  • 4
    7/12
  • Show Answer
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Answer : 3. "3/4"
Explanation :

Answer: C) 3/4 Explanation: Let A, B, C be the respective events of solving the problem and A , B, C be the respective events of not solving the problem. Then A, B, C are independent event ∴A, B, C are independent events Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4  PA=12, PB=23, PC= 34 ∴ P( none  solves the problem) = P(not A) and (not B) and (not C)                     = PA∩B∩C                    = PAPBPC         ∵ A, B, C are Independent                                          =  12×23×34                     = 14   Hence, P(the problem will be solved) = 1 - P(none solves the problem)                  = 1-14= 3/4

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