TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/1.2

Poker game

A deck of 52 cards has 13 ranks (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A) and 4 suits (♥, ♠, ♦, ♣). A poker hand is a set of 5 cards randomly chosen from a deck of 52 cards.

(a) A full house in poker is a hand where three cards share one rank and two cards share another rank. How many ways are there to get a full-house? What is the probability of getting a full-house?

(b) A royal flush in poker is a hand with ten, jack, queen, king, ace in a single suit. What is the probability of getting a royal flush?

Lösungsvorschlag von Gittenburg

--Gittenburg 20:56, 12. Okt. 2019 (CEST)

a) $13\cdot {\binom {4}{3}}\cdot 12\cdot {\binom {4}{2}}=3,744$ ways to get a full-house

There are ${\binom {52}{5}}=2,598,960$ possible hands.

$P({\text{full house}})=3,744/2,598,960\approx 0.00144$

b) $P({\text{royal flush}})=4/2,598,960\approx 0.000001539$