All Questions
Tagged with card-games solution-verification
15
questions
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From 52 cards, we draw N times with the return of 1 card each. Expected value of the number of different cards that were drawn. Solution verification
From a deck of 52 cards, we draw N times with the return of one card each. Calculate the expected value of the number of different cards that were drawn.
To calculate the expected value of the number ...
- 1,052
3
votes
1
answer
181
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Expected value of highest card before first ace
For practice, I decided to invent a variation on the problem of the expected number of cards to be drawn until the first ace is found. I would appreciate some feedback and clarification on certain ...
- 2,466
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162
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Draw 5 cards from a deck of 52 without replacement, what is the probability that those 5 cards are in ascending or descending order?
Need help double checking the answer for this one:
Firstly, calculate the probability of getting 5 distinct cards. This would be:
52/52 * 48/51 * 44/50 * 40/49 * 36/48 = p
Now, the probability of the ...
- 11
1
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1
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205
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Probability of picking 4 Aces in 10 Playing cards.
I have 52 Playing cards (no joker). I remove 2 cards randomly and remain with 50 cards. After that, I pick 10 cards of 50 cards. Calculate the probability of there being 4 Aces in 10 cards.
I solve ...
- 208
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1
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60
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Probability that a chosen card is greater than another chosen card, mistake in my "proof"
I want to solve this problem.
Consider a deck of 52 cards, ordered such that Ace > King > Queen > ... > 2. I pick a card, then you pick one. What is the probability that my card is larger ...
- 73
2
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0
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287
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Probability of everyone having 4333 distribution in bridge hand with given information
In a game of bridge, there are $4$ players, each is dealt a hand of $13$ cards coming from $4$ suits each of which has $13$ cards in that suit. We say that a player has a 4333 distribution if they ...
- 2,295
1
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1
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596
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A Problem dealing with a Deck of Cards and the Hypergeometric Distribution
Problem:
If $13$ cards are to be chosen at random(without replacement), determine
the probability that (a) $6$ will be picture cards, (b) none will be
picture cards.
Answer: (a)
The probability that a ...
- 4,014
0
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0
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38
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Alternative solution to finding P(ace of spades is immediately drawn after first ace).
Context
I understand this proof and it is quite slick and throws up a counterintuitive result.
However, before looking at the solution, I tried my own ham-fisted approach of finding P(AoS immediately ...
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
2
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158
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Which of the two methods is correct and why?
Problem
A deck of card is shuffled then divided into two halves of 26 cards
each. A card is drawn from one of the halves, it turns out to be an
ace. The ace is then placed in the second half-deck. The ...
- 901
1
vote
1
answer
197
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In how many different ways can you pick four cards so that your cards have exactly two suits?
Firstly, we pick which 2 suits we work with: 4 C 2
Secondly, there are three scenarios to consider:
Scenario 1: We pick 1 card from one suit and 3 from the other: 13 C 1 * 13 C 3
Scenario 2: We pick 2 ...
1
vote
2
answers
52
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Computing card probabilities
$1$ to $13$ and whose colors are red, green, blue, or yellow. You draw the topmost three cards. What's the probability that:
All three cards are green or blue. I think the answer is ${26\choose 3}/{...
user822241
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1
answer
102
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why is this method of calculating the probability of an ace wrong?
Problem: A deck of cards is shuffled and then divided into two halves of 26 cards each. A card is drawn from one of the halves; it turns out to be an ace. The ace is then placed in the second half-...
- 901
4
votes
1
answer
4k
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Solution verification: picking $5$-card hands from standard deck of $52$, with conditions
Problem
A 5-card hand is dealt from a perfectly shuffled deck of playing cards. What is the probability of each of the following events?
(a) The hand has at least one club.
(b) The hand has at least ...
- 3,023
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1k
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Five cards are chosen from a standard deck with replacement. Find joint PMF of number of queens, kings and others.
Five cards are randomly chosen from a standard deck, one at a time with replacement. Let $X$, $Y$, $Z$ be the numbers of chosen queens, kings, and other cards.
(a) Find the joint PMF of X, Y, Z.
...
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