a Remember to account for the intersection between clubs and face cards.
B
b The card you draw must be both a club and a face card.
C
c The probability is the complement to drawing a club or a face card.
A
aProbability: P(club or face card) = 1126
Union or intersection? This is an intersection.
B
bProbability: P(a club and a face card) = 352
Union or intersection? This is a union.
C
cProbability: P(not club and not face card)= 1526
Practice makes perfect
a Whenever we are looking for a probability of two or more events that involves the word or, we are looking for the union of those probabilities. To find this, we have to use the Addition Rule of Probability.
P(AorB)=P(A)+P(B)-P(A and B)The formula adds the probabilities of A and B and subtracts P(A and B), which describes the intersection of A and B. There are 13 clubs in the card. Also, each suit includes 3 face cards, so we have a total of 3(4)=12 face cards. However, 3 face cards are clubs, which is the intersection of drawing a club or a face card.
P(club)=13/52 [1em]
P(face card)=12/52 [1em]
P(club and face card)=3/52
With this we can calculate the probability of drawing a club or a face card.
b A club and a face card is the intersection of the probabilities of drawing a club or drawing a face card. From Part A we know that 3 cards of each suit are face cards, which means we can determine the probability of drawing a club and a face card.
P(a club and a face card) =3/52
c Note that this is the complement to the probability P(club or face card) which we found in Part A. Therefore, to find the probability of not drawing a club and not a face card, we can subtract the probability of drawing a club or a face card from 1.
