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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. 
      A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speed is?

    • Options
    • A. 4:1
    • B. 1.4
    • C. 2:1
    • D. 1:2
    • Discuss
    • 2. 
      The length of the train that takes 8 second to pass a pole where it runs at a speed of 36 km/hr is?

    • Options
    • A. 288 meters
    • B. 45 meters
    • C. 48 meters
    • D. 80 meters
    • Discuss
    • 3. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

    • Options
    • A. 12 sec
    • B. 24 sec
    • C. 48 sec
    • D. 60 sec
    • Discuss
    • 4. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

    • Options
    • A. 3.6 sec
    • B. 18 sec
    • C. 36 sec
    • D. 72 sec
    • Discuss
    • 5. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

    • Options
    • A. 48 km/hr
    • B. 54 km/hr
    • C. 66 km/hr
    • D. 82 km/hr
    • Discuss
    • 6. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

    • Options
    • A. 9 a.m.
    • B. 10 a.m.
    • C. 10.30 a.m.
    • D. 11 a.m.
    • Discuss
    • 7. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

    • Options
    • A. 12 sec
    • B. 24 sec
    • C. 48 sec
    • D. 60 sec
    • Discuss
    • 8. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

    • Options
    • A. Rs. 21,000
    • B. Rs. 22,500
    • C. Rs. 25,300
    • D. Rs. 25,800
    • Discuss
    • 9. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y =?

    • Options
    • A. 2 or 6
    • B. 4
    • C. 4 or 8
    • D. 8
    • E. None of these
    • Discuss
    • 10. The difference of the squares of two consecutive odd integers is divisible by which of the following integers?

    • Options
    • A. 3
    • B. 6
    • C. 7
    • D. 8
    • Discuss


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