Card Draw Experiment

A Card Draw Experiment is a Random Experiment that involves Cards with Symbols composed of the permutation of {A,2,3,4,5,6,7,8,9,10,J,Q,K} and {H,D,S,C} {i.e. (A,H),(A,D),...(K,C)} that are Randomly drawn (from a Card Deck), and whose Random Experiment Outcome is the 2-Tuple symbol on the drawn card.

• AKA: Card Draw.
• Context:
  • It can involve:
    • a Unbiased Card Deck (Fair Card Deck).
    • an Biased Card Deck (Unfair Card Deck).
  • It can be associated with a Card Draw Trial.
  • It can involve additional Cards, e.g. 'Joker Card'.
• Example(s):
  • Select a single card from a single Card Deck:
    • Example Outcome: (4,Diamond)
    • Sample Space = 13x4 = 52 Outcomes.
    • Event Space = 2⁵²=4,503,599,627,370,496 Events.
  • Select two cards from a single Card Deck stack:
    • Example Outcome: {(4,Diamond), (A,Heart)}
    • Sample Space = ChoseNoR(2,52) = 1,326 Outcomes (52!/50!/2!)
    • Event Space = {{},{(AH,2D)},{(JH,JD)} … {(2,S),(3,D)} … } with 2¹³²⁶ Events.
  • Select five cards from a Two Card Deck stack.
    • Example Outcome: {(Ace,Diamond)x2, (3,Heart)x1, (3,Diadmond)x1, (3,Spade)x1}
• Counter-Example(s):
  • a Sequential Random Experiment.
    • Toss a coin two consecutive times, roll a dice two times, and draw one card from a card deck.
• See: Coin Toss Experiment, Dice Roll Experiment, Random Sample Without Replacement.

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References

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Combinations#Number_of_k-combinations_from_a_set
  • For example, the number of five-card hands possible from a standard fifty-two card deck is:
    • {52 \choose 5} = \frac{n!}{k!(n-k)!} = \frac{52!}{5!(52-5)!} = \frac{52!}{5!47!} = 2,598,960.

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