A standard deck of 52 playing cards contains four of each numbered card 2 ce bond negative 10 and four each of aces, kings, queens, and jacks. Two cards are chosen from the deck at random. Which expression represents the probability of drawing a king and a queen?
Answer
A
the fraction with numerator open paren sub 4 cap c sub 1 close paren times open paren sub 3 cap c sub 1 close paren and denominator sub 52 cap c sub 2
B
the fraction with numerator open paren sub 4 cap p sub 1 close paren times open paren sub 4 cap p sub 1 close paren and denominator sub 52 cap p sub 2
C
the fraction with numerator open paren sub 4 cap c sub 1 close paren times open paren sub 4 cap c sub 1 close paren and denominator sub 52 cap c sub 2
D
the fraction with numerator open paren sub 4 cap p sub 1 close paren times open paren sub 3 cap p sub 1 close paren and denominator sub 52 cap p sub 2
Explanation
There are 4 kings and 4 queens, so the number of favorable pairs is (4 C 1)(4 C 1): choose one king and one queen. Since the two cards are chosen without regard to order, the total number of possible pairs is 52 C 2. Thus the expression is (4 C 1)(4 C 1) divided by (52 C 2), which is choice D.
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