Question
Two cards are drawn together from a pack of 52 cards . The probability that one is a spade and one is a heart , is :
Answer: Option D
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Let S be the sample space . Then
n(S) = `52_ (C _ 2) = ((52 xx 51))/((2 xx 1)) ` = 1326
Let E = event of getting 1 spade and 1 heart.
`:.` n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 .
= `(13_ (C_ 1) xx 13_ (C _ 1))` = ( 13 x 13) = 169
`:.` P (E) = `(n(E))/(n(S)) = 169/1326 = 13/102`
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