What is the Probability of Drawing Specific Combinations from a Deck of Cards?

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SUMMARY

The discussion focuses on calculating the probabilities of drawing specific combinations from a deck containing 4 aces and 2 kings. The probability of drawing exactly 3 aces when selecting 3 cards is determined to be 1/5. Additionally, the discussion emphasizes the importance of considering the order of drawing cards and suggests using a tree diagram for clarity. The calculations for drawing exactly 1 king and 2 aces, as well as exactly 2 kings and 1 ace, follow similar probabilistic reasoning.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with combinatorial mathematics
  • Knowledge of the "Or rule" in probability
  • Ability to create and interpret tree diagrams
NEXT STEPS
  • Study combinatorial probability techniques
  • Learn about the "Hypergeometric distribution" for drawing without replacement
  • Explore advanced probability concepts such as conditional probability
  • Practice creating tree diagrams for various probability scenarios
USEFUL FOR

This discussion is beneficial for students studying probability, educators teaching combinatorial mathematics, and anyone interested in understanding card game probabilities.

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Homework Statement


Suppose u have a deck composed of 4 aces and 2 kings. Find P(exactly 3 aces when u draw 3 cards), P(exactly 1 king and 2 aces when u draw 3 cards), and P(exactly 2 kings and 1 ace when u draw 3 cards).


Homework Equations





The Attempt at a Solution


P(exactly 3 aces when u draw 3 cards)=4/6*3/5*2/4=1/5
 
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benorin said:
P(exactly 3 aces when u draw 3 cards)=4/6*3/5*2/4=1/5

You do the same thing for (exactly 1 king and 2 aces when u draw 3 cards) and (exactly 2 kings and 1 ace when u draw 3 cards). However, you will have to consider the order of taking kings and aces. You will need Or rule too.
Drawing a tree diagram is very helpful
 
Last edited:

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