[\dfrac{13}{102}] Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is

For Competitive Exams

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

$ \dfrac{3}{20} $

$ \dfrac{29}{34} $

$ \dfrac{47}{100} $

$ \dfrac{13}{102} $

Explanation:

Let S be the sample space.

Then, $ n \left(S\right)$ = ⁵²C₂ =$ \dfrac{(52 \times 51)}{(2 \times 1)} $= 1326.

Let E = event of getting 1 spade and 1 heart.

$\therefore n \left(E\right)$= number of ways of choosing 1 spade out of 13 and 1 heart out of 13

=(¹³C₁ ¹³C₁)

= $\left(13 \times 13\right)$

= 169.

$\therefore P\left(E\right)$ =$ \dfrac{n(E)}{n(S)} $=$ \dfrac{169}{1326} $=$ \dfrac{13}{102} $.

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