Respuesta :
The probability that a five-card poker hand does not contain the queen of hearts is 47/52.
We have been given that,
Total card to choose = 5
Total cards in a deck = 52
We need to find the probability that a five-card poker hand does not contain the queen of hearts.
The total ways of choosing 5 cards from a deck of 52 cards = [tex]^{52}C_5[/tex]
The number of queens of hearts in a deck = 1
The number of cards excluding queens of hearts = 52 - 1
= 51
The total ways of choosing 5 cards from 51 cards = [tex]^{51}C_5[/tex]
Now we find the required probability.
[tex]\Rightarrow P= ^{51}C_5 \times ^{52}C_5\\\\\Rightarrow P=\frac{51!}{5!(51-5)!} ~\times \frac{52!}{5!(52-5)!}\\\\\Rightarrow P=\frac{47}{52}[/tex]
Therefore, the probability that a five-card poker hand does not contain the queen of hearts is 47/52.
Learn more about the probability here:
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