Card game probability question

In summary, the conversation discusses a card game where 5 players are dealt three types of cards and must match them with a counter. The probability that all players have the type A card matching their counter is (1/6)*(4/18)^3 *(3/18)^2 or 1/360. One player having two type A cards was not taken into consideration.
  • #1
jj975
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A card game involves dealing 3 types of cards to players. There are 6 type A cards, 9 type B cards and 6 type C cards. Each type A card has one matching counter.

In a game with 5 players, one card of each type is selected at random and hidden without knowledge. Each player then chooses a counter with one left over. All the remaining three types of card are combined, shuffled and dealt as evenly as possible to the players.

What is the probability that all of the 5 players have the type A card that matches their counter?




My solution:
Probability that the left over counter matches the hidden type A card = 1/6

18 of the three card types are dealt with three players receiving 4 cards and two players receiving 3 cards.

Probability of each player receiving the correct type A card = 4/18 and 3/18 respectively so the total probability that all players have the type A card matching their counter is
(1/6)*(4/18)^3 *(3/18)^2

Dues this seem correct to anybody? I was expecting this problem to be a lot harder so not sure if I'm missing something/done something wrong. Thanks in advance
 
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  • #2
I would have thought that since one player has two cards of type A then the answer would simply be (1/6)*(1/5)*(1/4)*(1/3)
 

What is a card game probability question?

A card game probability question is a type of question that involves calculating the likelihood of certain outcomes or events in a card game. It usually involves understanding the rules of the game and using mathematical principles to determine the probability of certain outcomes.

How do you calculate the probability of winning a card game?

To calculate the probability of winning a card game, you need to first understand the rules of the game and the number of cards in the deck. Then, you can use the formula: probability of winning = number of desired outcomes / total number of possible outcomes. This will give you a percentage which represents your chance of winning.

What is the difference between theoretical probability and experimental probability in card games?

Theoretical probability is the probability calculated using mathematical principles and the rules of the game. It is based on the assumption that every possible outcome is equally likely. Experimental probability, on the other hand, is based on actual experiments or trials of the game. It may differ from theoretical probability due to chance or imperfect conditions.

How does the number of players in a card game affect the probability of winning?

The number of players in a card game can significantly affect the probability of winning. In a game with more players, the chances of getting the desired cards decreases as there are more people to compete with. This makes the probability of winning lower compared to a game with fewer players.

What are some strategies for increasing the probability of winning a card game?

Some strategies for increasing the probability of winning a card game include understanding the rules and probabilities of the game, keeping track of cards that have already been played, and using probability calculations to make informed decisions. Additionally, knowing when to take risks and when to play conservatively can also improve the chances of winning.

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