JEE Main & Advanced Mathematics Probability Question Bank Odds in favour and odds against Addition theorem on probability

  • question_answer
    One card is drawn from a pack of 52 cards. The probability that it is a queen or heart is                                            [RPET 1999]

    A)                 \[\frac{1}{26}\]    

    B)                 \[\frac{3}{26}\]

    C)                 \[\frac{4}{13}\]    

    D)                 \[\frac{3}{13}\]

    Correct Answer: C

    Solution :

                       Probability that it is queen \[P(A)=\frac{4}{52}=\frac{1}{13}\]                    Probability  that it is heart \[P(B)=\frac{13}{52}=\frac{1}{4}\]                    Probability that it is queen and heart \[P(A\cap B)=\frac{1}{52}\]                    \[\therefore \] P (Queen or heart) \[=P(A)+P(B)-P(A\cap B)\]                                 \[=\frac{1}{13}+\frac{1}{4}-\frac{1}{52}\]\[=\frac{4+13-1}{52}\]\[=\frac{16}{52}=\frac{4}{13}\].


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