Question

Draw one card at random from a standard deck of cards. the sample space s is the collection of the 52 cards. assume that the probability set function assigns 1/52 to each of the 52 outcomes. let a = {x: x is a jack, queen, or king}, b = {x: x is a 9, 10, or jack and x is red}, c = {x: x is a club}, d = {x: x is a diamond, a heart, or a spade}.

Answer 1

In probability problems, look out for the word OR and AND.

OR means adding the probability
AND means multiplying the probability

P(a) = P(jack) + P(queen) + P(king) = (4/52) + (4/52) + (4/52) = 12/52 = 3/13

P(b) = [P(9) + P(10) + P(jack)] × P(red) = [(4/52) + (4/52) + (4/52)] × (26/52)
P(b) = (12/52) × (26/52) = 3/26

P(c) = 13/52 = 1/4

P(d) = P(a diamond) + P(a heart) + P(a spade) =  (13/52) + (13/52) + (13/52) = 3/4