Question

7.4-17 When a single card is drawn from an ordinary 52-card deck, find the probability of getting a red 7 or a black 8.

Answer 1

solution:

total number of cards in a deck = 52

number of black cards = 26 (13 of club and 13 of spades)

number of red cards = 26 ( 13 of heart and 13 of diamond)

let A be the event of drawing a red 7

and B be the event of drawing a black 8

number of red 7 in the deck = 2 (one is heart seven and one is diamond seven)

so P(A) = 2/52

number of black 8 in the deck = 2 ( one is club 8 and one is spade 8)

so P(B) = 2/52

so probability of drawing a red seven or black 8 = P(A u B)

both events are mutually exclusive, so P(A n B) = 0

P(A u B) = P(A) + P(B) - P(A n B)

P(A u B) = (2/52) + (2/52) = 4/52 = 1/13

co;rrect option is D: 1/13