A poker hand consists of 5 cards. The sample space has (552) possible outcomes.
a. Choose 3 kings from 4 kings. From the remaining 52−4=48 cards choose 2 non-kings to make a five-card poker hand
P(3 kings)=(552)(34)(5−352−4)=
=5!(52−5)!52!3!(4−3)!4!⋅2!(48−2)!48!=
=52(51)(50)(49)(48)2(48)(47)(120)=5414594≈0.001736
b. There are total 13 hearts and 13 diamonds.
Choose 4 hearts from 13 hearts
(413) Choose 1 diamonds from 13 diamonds
(113)
P(4 hearts and 1 diamonds)=(552)(413)(113)=
=5!(52−5)!52!4!(13−4)!13!⋅1!(13−1)!13!=
=52(51)(50)(49)(48)13(12)(11)(10)(5)(13)=39984143≈0.003576
Comments
Leave a comment