All Questions
Tagged with card-games inclusion-exclusion
15
questions
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Probability of Ace and King of same suit and probability of quads
Compute the probability that a
hand of 13 cards contains
(a) the Ace and King of at least one suit;
(b) all 4 of at least 1 of the 13 denominations.
Below, you will see the work that I had for this ...
1
vote
3
answers
290
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If I deal 7 cards what is the probability that there is at least one card from each suit.
I thought that this would be an easy problem, and it seems really obvious to me that the answer would be:
$$ \frac{\binom{13}{1}^4 \binom{48}{3}}{\binom{52}{7}} $$
but for some reason this comes out ...
- 122
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1
answer
267
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How many ways to pick two cards without replacement?
From the deck of 52 cards, in how many ways two cards can be picked such that the first card is spades and second card is not a face card.
My try: Here we can have two cases.
Case 1. First card is not ...
- 1,271
3
votes
1
answer
71
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Probability of the first card of a standard deck being a king or a heart.
I am solving an equation to find the probability that the first card of a standard, 52 card deck is a king or a heart, and I feel like I���m doing this wrong.
I set up this equation (k for king, h for ...
- 31
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1
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30
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The Principle of inclusion and exclusion to find probability [closed]
A 5-card hard is dealt from a standard deck of 52 cards. Find the Probability of at least 1 heart and 1 spade is among the 5 cards, Using Inclusion and exclusion.
So far I have 52C5-2*47C5 (47C5 from ...
1
vote
2
answers
58
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$9$-card-long (or longer) straight flush in a $13$-card hand
The other day at an online bridge site I got dealt a $13$-card hand containing $3,4,5,6,7,8,9,10,J$ of spades, i.e. a $9$-card-long straight-flush (s-f). This is so rare that I decided to count how ...
- 15.4k
2
votes
3
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267
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Combinatorics problem - choosing $6$ cards out of $32$-card deck so that there are exactly three different suits (Inclusion-Exclusion)
Suppose we have a deck of $32$ cards with $8$ cards of each of the four suits. In how ways we can choose six cards such that there are cards of exactly three different suits among the chosen cards?
I ...
1
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2
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166
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What's the probability for a 14-card hand to contain at least one full-house?
(This question is related to my previous question: When drawing 14 cards from a set of 52 cards, is it more likely to have a full house or two consecutive pairs?).
Problem: What is the probability ...
- 371
1
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2
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249
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We turn cards simultaneously from two well shuffled decks. Exact match means same card from each deck. Find probability of at least one exact match.
Problem
Suppose we turn over cards simultaneously from two well shuffled decks of ordinary playing cards. We say we obtain an exact match on a particular turn if the same card appears from each deck; ...
- 1,651
1
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1
answer
171
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Probability that duplicates are still in the deck after X card drawn
Deck has 30 cards, out of which 5 cards have duplicates (20 cards are unique, 5 cards have 2 copies each).
If you draw X cards from the deck (without returning), what is the probability that there ...
- 111
3
votes
2
answers
166
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3 people dealt 3 cards, probability that nobody recieves 3 of a kind
If $3$ people are dealt $3$ cards from a standard deck, determine the probability that none of them is dealt three of a kind?
Here is my attempt:
The total number of hands is
$${_{52}\mathsf C}_3\...
- 41
1
vote
1
answer
170
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How to calculate the probability of getting at least one of each card in a given set from a deck?
I am trying to calculate the probability of getting a particular straight after drawing $x$ cards from a deck. Say, for this example, that the straight I am attempting to obtain is "2-3-4-5-6". I know ...
- 346
7
votes
2
answers
925
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Probability question involving sets of cards
I have an infinite deck built out of sets of 10 cards (in other words 10*n cards). The sets are identical so one '2' is identical to another '2'.
A player draws 6 cards. If he draws:
any '1' AND a '...
- 71
13
votes
2
answers
5k
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Losing at Spider Solitaire
Spider Solitaire has the property that sometimes none of the cards in the final deal can "go" and so you lose, regardless of how much progress you have made beforehand. You would have known that you ...
- 3,075
2
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2
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non-routine application of inclusion-exclusion
What are the circumstances when inclusion-exclusion can't be routinely applied, and some adjustments have to be made ?
This question arises from a problem of finding the probability of getting a ...
- 42.7k