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Discussion :: Probability

  1. Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

    2. A.

    \( \frac {3 } { 20 } \)
    B.

    \( \frac { 29 } { 34 }\)
    C.

    \(\frac { 47} {100 }\)
    D.

    \(\frac { 1 3} { 102 } \)

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    Answer : Option D

    Explanation :

    Let S be the sample space.

     

    Then, n(S) = 52C2 = \(\frac { (52*51) } {( 2 *1)} \) =1326

     

    Let E = event of getting 1 spade and 1 heart.

     

    n(E)  = numbers of ways of chossing 1 spade out of 13 and 1 heart out of 13

         

            = (13C1 x 13C1)

         

            =  (13 x 13)

         

            = 169

     

      P(E) = \(\frac { n(E) } { n(S)} \) =\( \frac { 169 } { 1326 } \) =\(\frac { 1 3} { 102 } \)

     

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