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} $.