# math

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A single card is selected from an ordinary deck of cards. The sample space is shown in the following figure. Find the following probabilities. (Enter the answers either as fractions or as decimals rounded to three places.)

P(five of clubs) = 1
P(five) = 2
P(club) = 3
P(jack) = 4
P(five and a jack) = 7
P(five or a jack) = 8
P(heart and a jack) = 9
P(heart or a jack) = 10

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• math -

Because there's no sample space diagram here to clarify the point, my first question is "Does an ordinary deck of cards contain a joker?", because that affects the answer to every subsequent question. Assuming that it doesn't:
P(five of clubs): there's only one five of clubs in a deck, so the answer is 1/52.
P(five): there are four fives in a deck, so the answer is 4/52 = 1/13.
P(club): there are 13 clubs in a deck, so the answer is 13/52 = 1/4.
And so on. Note on question 7 that a single card can't be both a five and a jack.