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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 die blindfolded and asks abhay to tell him if the outcome is a prime abhay says, YES what is the probability that he outcome is really prime?

    A) 0.5

    B) 0.75

    C) 0.6

    D) None of these  

    Correct Answer: C

    Solution :

    [c] There are two cases when Abhay will say ?Yes?. Case (i) the number that come out is a prime and abhay is speaking truth, probability for this case is \[P(P)\times P(T)\] Here P (P) = Probability of getting a prime = 3/6 = ½ = 0.5 P (T) is probability that Abhay is speaking truth and P (T) = 0.6 So probability for this case is\[0.5\times 0.6=0.3\]. Case (ii) The number that come out is not a prime and Abhay is not speaking truth, probability for this case is \[P(P')\times P(T')=0.5\times 0.4=0.2\] 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 0.3/0.5=0.6.


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