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

  • question_answer
    In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes, is [MNR 1988]

    A)                 \[\frac{1}{5}\]       

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

    C)                 \[\frac{1}{3}\]       

    D)                 \[\frac{2}{3}\]

    Correct Answer: B

    Solution :

               \[P(A)=\frac{40}{100},\] \[P(B)=\frac{25}{100}\] and \[P(A\cap B)=\frac{15}{100}\]                 So \[P\left( \frac{B}{A} \right)=\frac{P(A\cap B)}{P(A)}=\frac{15/100}{40/100}=\frac{3}{8}.\]


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