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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-II

  • question_answer
    Abhay speaks the truth only 60%. Hasan rolls a dice blindfolded and asks abhay to tell him if the outcome is a ?Prime?. Abhay says, ?No?. What is the probability that the outcome is really ?Prime??

    A) 0.5

    B) 0.75

    C) 0.6

    D) None of these

    Correct Answer: D

    Solution :

    [d] There are two cases when Abhay will say? No? Case (i) the number that come out is a prime and Abhay is not speaking truth, probability for this case is \[P(P)\times P(T').\] Here P (P) = probability of getting a prime =3/6=1/2=0.5 P (T) is probability that abhay is speaking truth and P (T) \[=0.6soP(T')=0.4\] So probability for this case is \[0.5\times 0.4=0.2\] Case (ii) the number that come out is not a prime and abhay is speaking truth, probability for this case is\[P(P')\times P(T)=0.5\times 0.6=0.3\]. So total probability for the given case is 0.3+0.2=0.5. New sample space is 0.5 and we have to find the probability of case (i) which is 0.2/0.5=0.4.


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