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) = 52C2 = \(\frac{(52\times51)}{(2\times1)}\) = 1326.
Let E = event of getting 1 spade and 1 heart.
So, n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13
= (13C1 x 13C1)
= (13 x 13)
= 169.
So, \(P(E) = \frac{n(E)}{n(S)}=\frac{169}{1326}=\frac{13}{102}.\)
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