# What Is the Probability of Having the Fourth Ace in a Card Game?

• truewt
In summary: This is an example of conditional probability, where the probability of an event is affected by the knowledge of a previous event. In summary, the probability of player Z having the 4th Ace in the rest of his hands is 10/49, and this is an example of conditional probability.
truewt
Hi guys.

A question came to me as I'm playing a card game with 4 players. Let's say the full deck (of 52 playing cards) are all dealt to each player, one at a time into player's hands in a direction. All the cards are fully dealt before a player views the cards in his hands.

Assume player Z picks up his hand and takes a look at the first 3 cards. They are all Aces. What will the probability of player Z having the 4th Ace in the rest of his hands (assuming he didn't see the rest of them). Will it be conditional probability, or will the probability be equivalent to that of player Z holding all 4 Aces, regardless of him looking at the first 3 cards or not?

And what will be the solution to the probability be like? Sorry I wanted to attempt at this problem, but seems that there's also this chance that the other players get an Ace, hence it would be incorrect to say the probability of getting the 4 Aces is that simple?

Assume player Z picks up his hand and takes a look at the first 3 cards. They are all Aces. What will the probability of player Z having the 4th Ace in the rest of his hands (assuming he didn't see the rest of them). Will it be conditional probability, or will the probability be equivalent to that of player Z holding all 4 Aces, regardless of him looking at the first 3 cards or not?

Since Z has 3 aces, the probability of having the fourth ace is 10/49. This is much higher than the probability of having all four aces sight unseen.

## 1. What is the probability of getting a specific card in a deck?

The probability of getting a specific card in a deck is 1 in 52, or approximately 1.92%. This is because there are 52 cards in a deck and each card has an equal chance of being drawn.

## 2. What is the probability of getting a certain hand in a card game?

The probability of getting a certain hand in a card game depends on the specific game being played and the number of cards in the deck. For example, the probability of getting a royal flush in a game of Texas Hold'em with a standard 52-card deck is approximately 0.0002%.

## 3. How can I calculate the probability of winning in a card game?

To calculate the probability of winning in a card game, you need to know the number of cards in the deck, the number of cards in your hand, and the number of cards that will result in a win. You can then use the formula (number of cards that will result in a win / total number of possible outcomes) to determine the probability of winning.

## 4. How does the number of players in a game affect the probability of winning?

The number of players in a game can affect the probability of winning in a card game. For example, in a game of poker, the more players there are, the higher the chances of someone having a better hand than you. This decreases your overall probability of winning.

## 5. What is the difference between theoretical probability and experimental probability in a card game?

Theoretical probability refers to the probability of an event occurring based on mathematical calculations, while experimental probability is based on actual results from trials or experiments. In a card game, theoretical probability can be used to calculate the overall chances of winning, while experimental probability can be used to analyze the actual outcomes of a specific game or hand.

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