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5-45.

In a standard deck of $52$ playing cards, $13$ cards are clubs, and $3$ of the clubs are “face” cards (K, Q, J). What is the probability of drawing one card that is:

1. A club or a face card? Is this a union or an intersection?

The Addition Rule is $P(\text{A or B})=P(\text{A})+P(\text{B})-P(\text{A and B})$.
Remember a union is the cards that can be found in both events, where the intersection is the cards they have in common.

$P(\text{club or face})=P(\text{club})+P(\text{face})−P(\text{club and face})$

Refer to the Math Notes box in Lesson 4.2.4 for more assistance.

2. A club and a face card? Is this a union or an intersection?

$\array{P(\text{club and face})=\frac{\text{number of clubs that are face cards}}{\text{total number of cards}}}$

$\frac{3}{52}; \text{ intersection}$

3. Not a club and not a face card?

This question is asking for the complement of part (a).
A complement is all outcomes that are not part of the original set of outcomes.