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

  • question_answer
    Three coins are tossed. If one of them shows tail, then the probability that all three coins show tail, is

    A)                 \[\frac{1}{7}\]       

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

    C)                 \[\frac{2}{7}\]       

    D)                 \[\frac{1}{6}\]

    Correct Answer: A

    Solution :

                      Let \[E\] be the event in which all three coins shows tail and \[F\] be the event in which a coin shows tail.                   \ \[F=\{HHT,\,HTH,\,THH,\,HTT,\,THT,\,TTH,\,TTT\}\]                   and \[E=\{TTT\}\].                 Required probability \[=P(E/F)=\frac{P(E\cap F)}{P(E)}=\frac{1}{7}.\]


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