Question

In a 7​-card ​poker, played with a standard​ 52-card deck, 52C7​, or 133,784,560​, different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by . Shown to the right is the number of ways a particular type of hand can occur and its associated probability. Find the probability of not being dealt this type of hand.

Answer 1

The probability of being dealt a bridge hand that does not contain a heart from a standard 52-card deck is approximately 0.0128, or 1.28%, which is the result of dividing the number of ways to choose 13 non-heart cards (39C13) by the total number of ways to choose 13 cards from the deck (52C13).

Step-by-step explanation:

To calculate the probability of being dealt a bridge hand without a heart from a standard 52-card deck, we need to consider the total ways to choose 13 cards from the 52 cards, and then find how many of these ways exclude hearts. Since there are 13 cards in each suit, and we're excluding hearts, we're choosing from the 39 non-heart cards.

The total number of ways to pick 13 cards from 52 is calculated by the combination formula:

• 52C13 = 635,013,559,600

To compute the probability of a hand without a heart, we exclusively choose all cards from the remaining three suits:

• 39C13 = 8,122,425,444

Therefore, the probability of not being dealt a heart is the division of the two:

• P(No Heart) = 39C13 / 52C13
• P(No Heart) = 8,122,425,444 / 635,013,559,600
• P(No Heart) ≈ 0.0128, or 1.28%