Question

Texas hold ’em In popular Texas hold ’em variety of poker, players make their best five-card poker hand by combining the two cards they are dealt with

three of five cards available to all players. You read in a book on poker that if you hold a pair (two cards of the same rank) in your hand, the probability of getting four of a kind is $88/1000$

(a) Explain what this probability means.

(b) Why doesn’t this probability say that if you play

1000 such hands, exactly $88$will be four of a kind?

Short answer

Part (a) Out of $1000$poker hands with a pair, around $88$of them have a four of a kind.

Part (b) Out of 1000poker hands with a pair, we estimated that $88$of them contained a four of a kind.

Step-by-step solution

Part (a) Step 1. Given Information

Getting four of a kind has a $0.25$chance of happening.

Part (a) Step 2. Concept

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The probability of a chance outcome is its long-run relative frequency.

Part (a) Step 3. Explanation

The probability mentioned in the question is 88/1000, which suggests that out of every 100 poker hands with a pair, we should expect 88 of them to have a four-of-a-kind. This is the meaning of the probability given in the question for various Texas hold 'em poker games.

Part (b) Step 1. Explanation

This probability does not guarantee that out of 1000 such hands, exactly 88 will be four of a kind because it is also possible that 87 or 89 will be four of a kind. The number of fours of a kind is usually close to 88, but it isn't always exactly 88.