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JEE Main & Advanced Mathematics Probability Question Bank Conditional probability bayes theorem

  • question_answer
    A biased die is tossed and the respective probabilities for various faces to turn up are given below
     Face : 1 2 3 4 5 6
     Probability : 0.1 0.24 0.19 0.18 0.15 0.14
    If an even face has turned up, then the probability that it is face 2 or face 4, is [MNR 1992]

    A)                 0.25       

    B)                 0.42

    C)                 0.75       

    D)                 0.9

    Correct Answer: C

    Solution :

               Let \[A\] be the event that even face turns up and \[B\] be the event that it is 2 or 4.            Then\[P(A)=P(2)+P(4)+P(6)=0.24+0.18+0.14=0.56\]               \[P(B)=P(2)+P(4)=0.24+0.18=0.42\]                 So, \[P(B/A)=\frac{P(B\cap A)}{P(A)}=\frac{P(B)}{P(A)}=\frac{0.42}{0.56}=0.75\].


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