### Home > INT2 > Chapter 3 > Lesson 3.2.1 > Problem3-73

3-73.

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 event a union or an intersection?

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

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

Refer to the Math Notes box in Lesson 3.1.5 for more assistance.

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

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

$\frac{3}{52};$ 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.
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