Question

9. What is the probability that a five-card poker hand does not contain the queen of hearts?
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Answer 1

Answer:

47/52 is the probability

Step-by-step explanation:

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Answer 2

Given,

Total card to choose = 5

Total cards in a deck = 52

To Find,

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

Solution,

The total ways of choosing 5 cards from a deck of 52 cards = 52C5

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 = 51C5

The probability = 51C5 / 52C5 = 51!/(5!*46!) * (5!*47!)/52!

The probability = 47/52

Hence, the probability that a five-card poker hand does not contain the queen of hearts is 47/52.