Suppose we shuffle a deck and draw the top card. What is the probability that this card is a red card or a face card (or possibly both)?
+2446 Assuming we are dealing with standard playing cards and we are ignoring jokers, then 26 out of the 52 cards are red. 12 cards (Jacks, Queens, and Kings) are face cards. 6 cards are both red and a face card, so we must subtract these to avoid double-counting these.
\(P(\text{red} \cup \text{face})=P(\text{red})+P(\text{face})-P(\text{red}\cap\text{face})\\ P(\text{red} \cup \text{face})=\frac{26}{52}+\frac{12}{52}-\frac{6}{52}\\ P(\text{red} \cup \text{face})=\frac{32}{52}=\frac{8}{13} \)
