TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/1.2: Unterschied zwischen den Versionen

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:(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?
 
:(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?
  
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== Lösungsvorschlag von [[Benutzer:Gittenburg|Gittenburg]] ==
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--[[Benutzer:Gittenburg|Gittenburg]] 20:56, 12. Okt. 2019 (CEST)
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a) <math>13 \cdot \binom43 \cdot 12 \cdot \binom42=3,744</math> ways to get a full-house
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There are <math>\binom{52}5=2,598,960</math> possible hands.
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<math>P(\text{full house}) = 3,744/2,598,960 = 0.00144</math>
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b) <math>P(\text{royal flush}) = 4/2,598,960 = 0.000001539</math>

Version vom 12. Oktober 2019, 20:56 Uhr

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 \binom43 \cdot 12 \cdot \binom42=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 = 0.00144

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