# Two Cards Are Drawn Together from a Pack of 52 Cards. the Probability that One is a Spade and One is a Heart, is - Mathematics

MCQ

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

• 3/20

• 29/34

• 47/100

• 13/102

#### Solution

13/102

Explanation:
Let S be the sample space.

Then, n(S) = ""^52C_2=((52xx51))/((2xx1))=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.

= (""^13C_1xx""^13C_1)

= (13 x 13) = 169

∴ P(E) = (n(E))/(n(S))

= 169/1326=13/102

Concept: Probability (Entrance Exam)
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