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

  • question_answer
    A coin is tossed three times in succession. If E is the event that there are at least two heads and F is the event in which first throw is a head, then \[P\,\left( \frac{E}{F} \right)=\]    [MP PET 1996]

    A)                 \[\frac{3}{4}\]       

    B)                 \[\frac{3}{8}\]

    C)                 \[\frac{1}{2}\]       

    D)                 \[\frac{1}{8}\]

    Correct Answer: A

    Solution :

               \[S=\{HHH,\,HHT,\,HTH,\,THH,\,HTT,\,THT,\,TTH,\,TTT\]            \[n\,(E)=4,\,\,n\,(F)=4\] and \[n\,(E\cap F)=3\]                 \[\therefore \,\,\,P\left( \frac{E}{F} \right)=\frac{P(E\cap F)}{P(F)}=\frac{3/8}{4/8}=\frac{3}{4}.\]


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