# If 2 cards are drawn from a deck of cards, how do you find P(heart or club)?

Dec 25, 2014

The above explains the probability of drawing a heart or club in one draw very well. Now let's move over to P(heart or club) when drawing two cards.

This is a bit more complicated. There are two possibilities:
(1) You've already drawn a 'right' at the first draw $P \left(1 s t R i g h t\right) = \frac{1}{2}$
as explained above

(2) You didn't. $P \left(1 s t W r o n g\right) = \frac{1}{2}$
Then there are 51 cards left: 26 'rights' and 25 'wrongs'. Probability of getting a 'right' in the second draw $P = \frac{26}{51}$ multiply by the first being wrong.
So $P \left(1 s t W r o n g , 2 n d R i g h t\right) = \frac{1}{2} \cdot \frac{26}{51} = \frac{26}{102}$

You may add the probabilities of cases (1) and (2):
$P \left(H \mathmr{and} C\right) = \frac{51}{102} + \frac{26}{102} = \frac{77}{102} = 0.7549$ (two cards)