V63.0233, Theory of Probability Name:
Worksheet for Section 2.5 : Sample spaces having equally likely outcomes July 6, 2009
A poker deck consists of 52 cards. Each card is marked with a suit—one of hearts (♡), spades (♠),
clubs (♣), or diamonds (♢), and a rank —a number from 2 through 10, or Jack (J), Queen (Q),
King (K), or (A). For purposes of ordering, J is equivalent to 11, Q to 12, and K to 13. A can be
considered 1 or 14 as necessary.
1. Suppose five cards are dealt from the deck. Find the probabilities of the following hands.
Each hand should be assumed to be no better than stated (e.g., a hand of three twos is also a hand
of a pair of twos, but that’s not useful)
(i) a pair of twos
Hint. Consider as the equally likely outcomes the set of five-card hands dealt from the 52 in
the deck. If these hands are counted without regard to order, then the number of favorable
hands can also be counted without regard to order. So, for instance, in this problem you
could assume the “favorable” hands have the first two cards being twos, and the last three
non-twos, with no pair among the last three, either.
(ii) any pair
(iii) two pair
(iv) three sixes
(v) three of any kind
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(vi) a straight (five cards of consecutive ranks. Notice according to the rules that A-2-3-4-5 and
10-J-Q-K-A are straights, but not Q-K-A-2-3. Also, five cards of consecutive ranks and the
same suit is another hand; read on)
(vii) a flush (five cards of the same suit)
(viii) a full house (three of one kind and two of another)
(ix) four of a kind
(x) a straight flush (five cards of the same suit in consecutive ranks)
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