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If it is assumed that all poker hands are equally likely,
Chapter 2, Problem 15P(choose chapter or problem)
If it is assumed that all \(\left(\begin{array}{c}52 \\5\end{array}\right)\) poker hands are equally likely, what is the probability of being dealt
(a) a flush? (A hand is said to be a flush if all 5 cards are of the same suit.)
(b) one pair? (This occurs when the cards have denominations a, a, b, c, d, where a, b, c, and d are all distinct.)
(c) two pairs? (This occurs when the cards have denominations a, a, b, b, c, where a, b, and c are all distinct.)
(d) three of a kind? (This occurs when the cards have denominations a, a, a, b, c, where a, b, and c are all distinct.)
(e) four of a kind? (This occurs when the cards have denominations a, a, a, a, b.)
Questions & Answers
QUESTION:
If it is assumed that all \(\left(\begin{array}{c}52 \\5\end{array}\right)\) poker hands are equally likely, what is the probability of being dealt
(a) a flush? (A hand is said to be a flush if all 5 cards are of the same suit.)
(b) one pair? (This occurs when the cards have denominations a, a, b, c, d, where a, b, c, and d are all distinct.)
(c) two pairs? (This occurs when the cards have denominations a, a, b, b, c, where a, b, and c are all distinct.)
(d) three of a kind? (This occurs when the cards have denominations a, a, a, b, c, where a, b, and c are all distinct.)
(e) four of a kind? (This occurs when the cards have denominations a, a, a, a, b.)
ANSWER:Step 1 of 5
a) We have to find the probability of being a flush
In poker hands there are 4 sets from that we have to choose one set
After that from that set of 13 we have to choose 5 cards
Selecting 5 cards from 52 cards is
Then P(flush) =
=0.0019
Hence the probability of flush is 0.0019