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  • Question
  • 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?


  • Options
  • A. 1/4
  • B. 1/2
  • C. 3/4
  • D. 7/12

  • Correct Answer
  • 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

      P A = 1 2 ,   P B = 2 3 ,   P C =   3 4

    ?  P( none  solves the problem) = P(not A) and (not B) and (not C)  

                      =  P A ? B ? C  

                      =  P A P B P C           ?   A ,   B ,   C   a r e   I n d e p e n d e n t                        

                      =   1 2 × 2 3 × 3 4   

                      =  1 4   

    Hence, P(the problem will be solved) = 1 - P(none solves the problem) 

                    =  1 - 1 4 = 3/4

  • Tags: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO

    More questions

    • 1. What value should come in place of the question mark(?) in the following question? (?) - 19657 - 33994 = 9999

    • Options
    • A. 63650
    • B. 53760
    • C. 59640
    • D. 61560
    • E. None of these
    • Discuss
    • 2. What value should come in place of the question mark(?) in the following question? (?) + 3699 + 1985 - 2047 = 31111

    • Options
    • A. 34748
    • B. 27474
    • C. 30154
    • D. 27574
    • E. None of these
    • Discuss
    • 3. What value should come in place of the question mark(?) in the following question?
      250 / √ ? = 10

    • Options
    • A. 25
    • B. 250
    • C. 625
    • D. 2500
    • Discuss
    • 4. What value should come in place of the question mark(?) in the following question?
      ? + 6207 - 9038 = 107

    • Options
    • A. 2724
    • B. 2938
    • C. 2814
    • D. None of these
    • Discuss
    • 5. What value should come in place of the question mark(?) in the following question?
      ? - 4799 = 1714

    • Options
    • A. 6513
    • B. 7403
    • C. 3085
    • D. None of these
    • Discuss
    • 6. What value should come in place of the question mark(?) in the following question?
      9501 -? = 3697

    • Options
    • A. 13198
    • B. 5814
    • C. 5804
    • D. 4894
    • Discuss
    • 7. What value should come in place of the question mark(?) in the following question?
      66066 + 6606 + 66 + 6 =?

    • Options
    • A. 258126
    • B. 72744
    • C. 72798
    • D. None of these
    • Discuss
    • 8. What value should come in place of the question mark(?) in the following question?
      ? x 48 = 173 x 240

    • Options
    • A. 545
    • B. 685
    • C. 865
    • D. 495
    • Discuss
    • 9. What value should come in place of the question mark(?) in the following question?
      ? x 11 = 555555

    • Options
    • A. 505
    • B. 5050
    • C. 50505
    • D. 5005
    • Discuss
    • 10. What value should come in place of the question mark(?) in the following question?
      87 x? = 3393

    • Options
    • A. 39
    • B. 49
    • C. 27
    • D. 67
    • Discuss


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