What is the Probability Each Player Receives One Black Card in a Card Game?

  • Thread starter Thread starter being_doug
  • Start date Start date
  • Tags Tags
    hand
Click For Summary
SUMMARY

The probability of each player receiving one black card in a card game with a well-shuffled deck of 4 black cards and 12 red cards is calculated using combinatorial methods. The total number of ways to deal 4 cards to 4 players from a deck of 16 is determined by the formula for combinations. The specific solution involves calculating the favorable outcomes where each player receives exactly one black card, which requires understanding the distribution of cards and the use of combinatorial coefficients.

PREREQUISITES
  • Combinatorial mathematics
  • Understanding of probability theory
  • Familiarity with card games and deck composition
  • Basic knowledge of the binomial coefficient
NEXT STEPS
  • Study combinatorial methods for calculating probabilities in card games
  • Learn about the binomial coefficient and its applications in probability
  • Explore the concepts of permutations and combinations in probability theory
  • Read "Intro to Probability" by Bertsekas and Tsitsiklis for detailed examples
USEFUL FOR

Students studying probability, mathematicians interested in combinatorial problems, and educators teaching probability concepts in card games.

being_doug
Messages
1
Reaction score
0

Homework Statement


A well shuffled deck has 4 black cards and 12 red cards (16 total). The cards are
dealt out to 4 players (each gets 4 cards). What is the probability that each player will have 1 black card?

Homework Equations



Asking how to set this up and solve this.

The Attempt at a Solution



There's a solution in the Bertsekas/Tsitsiklis "Intro to Probability" book for a similar problem, but I don't understand the explanation.
 
Last edited:
Physics news on Phys.org
In how many ways can you deal four cards to four people from a deck of 16?

In how many ways can you deal four cards to four people from a deck of 16 such that each receives exactly one black card?
 

Similar threads

Replies
2
Views
1K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
31
Views
6K
Replies
6
Views
2K