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}.

Question

Mathematics

Krystal Beard

12 December, 14:06

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}.

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Maxim Cain · 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