Two cards are drawn together from a pack of 52 cards. The probability that one i

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

Options:

A . 3 20

B . 29 34

C . 47 100

D . 13 102

Answer: Option D

Let S be the sample space.

Then, n(S) = ⁵²C₂ =
(52 x 51)
= 1326.
(2 x 1)

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
= (¹³C₁ x ¹³C₁)
= (13 x 13)
= 169.

P(E) =
n(E)
=
169
=
13
.
n(S)
1326
102

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