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

Options

• `3/20`

• `29/34`

• `47/100`

• `13/102`

Answer 1

`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`