Posted by admin | Posted in Uncategorized | Posted on 05-01-2004
Tags: card deck boxes, card deck holder, card deck images, card deck printing, card deck probability, card deck simulator, card deck tricks, card deck workout, card decks, card decks wow, cards, game, games, howto, magic
Card Deck
What are the odds of guessing one card in a deck?
What are the odds of guessing one card correctly in a 52 card deck. That includes getting the correct card and suit. are the odds 1:52?
Yes, if you’re guessing the suit and number it’s 1:52 (or 54 with jokers).
If you’re just guessing the suit or just the number, it’s 4:52 since there are four suits and four of each number. 4:52 is the same as 1:13.
With jokers it’s 4:54, which is 2:27.
Card Deck
A 5-card hand is randomly drawn from a standard 52-card deck. What is the probability of getting “three of a k?
A 5-card hand is randomly drawn from a standard 52-card deck. What is the probability of getting “three of a kind”?
First consider how many possible combinations of 5 card hands possible:
52C5 = 2598960
Now consider the combinations with 3 of a kind:
13C1 : which rank will the three of a kind be,
4C3 : of the rank chosen, which 3 cards will be picked
49C2: of the remaining 49 cards, pick two more to complete the hand,
so 13C1 * 4C3 * 49C2 = 61152
Your probability is: 61152/2598960 = 0.0235294 = 2.35%
Note, hands like full house and four of a kind are also considered for the probability calculated above. If you you only want the probability of three of a kind, (four of a kind, full house excluded) then you have to subtract the combinations for four of kind and full house from 61152.
For full house: 13C2 * 4C3 * 4C2 = 1872 combinations
(choose two ranks, one for three of a kind and one for pair, choose which 3 for three of a kind and choose which 2 for the pair)
For four of a kind: 13C1 * 4C4 * 48C1 = 624
(by similar arguments as the two above)
61152 – 1872 – 624 = 58656
So the probability of three of a kind ONLY is: 58656/2598960 = 0.022569 = 2.2569%
Wink Martindale – Deck of Cards (1959)
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