Answer to Question #155559 in Statistics and Probability for Abigail Jimenez

Question

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?
2. A club and a face card? Is this event a union or an intersection?
3. Not a club and not a face card?

Answer 1

Denote by CLUBS the event of drawing a club card and by FACE - the event of drawing a face card. Then there are 13 possibilities for CLUBS, 12 possibilities for FACE.

2) There are 3 possibilities for drawing a club and a face card. This event is an intersection of the events: CLUBS & FACE. Its probability is 3/52.

1) Drawing a club or a face card is a union of the events CLUBS OR FACE. To count the number of possibilities for this event we should add possibilities for CLUBS (13) and for FACE (12) and subtract possibilities for CLUBS & FACE (3). The total is 22, and the probability of this event is equal to 22/52.

3) Drawing not a club and not a face club is an intersection of events (NOT CLUBS) & (NOT FACE). This event is a complement to the event (CLUBS OR FACE). The number of the possibilities for this event is equal to 52 - 22 = 30 and the probability of this event is equal to 30/52.

Answer. 1) 22/52; 2) 3/52; 3) 30/52.