Answer :
Answer:
Step-by-step explanation:
The odds of selecting 5 cards from a deck of 52 are 52c5. Probability = Maximum outcomes / Possible outcomes for the given circumstance = 52!/47!*5! = 2598960. Now, in poker, the chance of selecting any two numbers from a pool of 13 distinct numbers is 13c2.
Possible poker hands
C(n,r)= C(52,5)
=52!/(5!(52-5!)
=2598960
Hand with pattern
(X,X,Y,Y,Z)
Number of choices for x and y
C(n,r)= C(13,2)
=13!(2!(13-2)!)
=78
Ways to get 2 X's
C(n,r)= C(4,2)= 4!(2!(4-2)!) =6
Similarly, ways to get 2x's is 6
We have 44 choice of occurance for Z
Hands with two pairs =78*44*6*6= 123552
So, Probability of Two pairs is =123552/2598960=0.047539
P(Two pairs) = 0.0475
How many ways can we choose two pairs in a poker hand?
There are 13 ways to choose the denomination of the first pair, 12 ways to choose the denomination of the second pair, and 4 choices for the remaining card. Thus, there are 13\cdot 12\cdot 4 = 624 ways to choose two pairs in a poker hand.
In poker, a hand is made up of 5 cards from a deck of 52 cards. The different possible hands in poker include a royal flush, straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, and one pair.
In this problem, we are asked to find the probability of getting a hand with two pairs.
To find the probability of two pairs, we first need to find the total number of possible poker hands. This is done using the combination formula C(n,r) where n is the total number of cards (52 in this case) and r is the number of cards needed to make a hand (5 in this case). This gives us a total of 2598960 possible poker hands.
Next, we need to find the number of possible hands with two pairs. A hand with two pairs has a pattern of X,X,Y,Y,Z where X and Y are the ranks of the pairs and Z is the remaining card. There are 13 ranks in a deck of cards (Ace, 2, 3, ..., 10, Jack, Queen, King) and we need to choose 2 of these ranks to be the ranks of the pairs. This can be done in C(13,2) ways, which is 78.
There are 4 cards of each rank in a deck, so there are 6 ways to choose the 2 cards of rank X and 6 ways to choose the 2 cards of rank Y.
Finally, we have 44 choices for the remaining card (Z) because there are 13 ranks and we have already used up 2 ranks for the pairs.
Therefore, the number of possible hands with two pairs is 78*6*6*44 = 123552. The probability of getting a hand with two pairs is then 123552/2598960 = 0.047539 or approximately 0.0475.
Therefore, the final answer is P(Two pairs) = 0.0475.
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Answer: The probability of receiving a hand with two pairs is 0.04322.
Step-by-step explanation:
How many ways are there in a poker hand to pick two pairs?
There are 13 ways to choose the denomination of the first pair, 12 ways to choose the denomination of the second pair, and 4 choices for the remaining card. Thus, there are 13*12*4 = 624 ways to choose two pairs in a poker hand.
In poker, a hand is made up of 5 cards from a deck of 52 cards. The different possible hands in poker include a royal flush, straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, and one pair.
To choose the denominations of the two pairings, there are C(13,2)=78 possible options. There are C(4,2)=6 methods to select the two cards in each pair for each of these approaches. The remaining card's denomination can be determined in C(4,1)=4 different ways. As a result, there are 78*6*6*4=11232 different ways to deal a hand with two pairs.
A hand of five cards can be dealt in C(52,5)=2598960 different ways. Therefore, the probability of receiving a hand with two pairs is 11232/2598960=0.04322.
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