What is the probability that a five-card poker hand does not contain the queen o

slaggingV

slaggingV

Answered question

2021-10-29

What is the probability that a five-card poker hand does not contain the queen of hearts?

Answer & Explanation

Malena

Malena

Skilled2021-10-30Added 83 answers

Definitions
Definition permutation
P(n,r)=n!(nr)!
Definition combination
C(n,r)=(nr)=n!r!(nr)!
with nn(n1)21
Complement rule:
P(E)=1P(E)
Solution A standart deck of cards contain 52 cards. A five-card poker hand selects 5 of the 52 cards.
C(52,5)=52!5!(525)!=52!5!47!=2,598,960
Numbers of hands with the queen of hearts
We select the queen of hearts and then we still need to select 4 of the remaining 51 cards
C(51,4)=51!4!(514!}=51!4!47!=249,900
Probability:
The probability is the number of favorable outcomes divided by the number of possible outcomes.
P=249,9002,598,960=552
=1552
=4752
0.9038
Result: 4752

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