What is the probability that a five card poker hand contains one ace?

This probability is (485)(525), for we have 48 choose 5 possible hands with no aces. Then the solution to the problem – that is, the probability of at least one ace appearing in a 5-card hand – is one minus the complement: 1−(485)(525).

How many possible 5 card hands are there in a standard 52 card deck?

2,598,960
Probability of a Full House First, count the number of five-card hands that can be dealt from a standard deck of 52 cards. We did this in the previous section, and found that there are 2,598,960 distinct poker hands.

What is the probability that a five card poker hand contains 5 cards all of a different rank?

So, the chance of getting a hand with five different kinds is about 1/2.

What is the probability that a five card poker hand has four aces?

If you have a standard deck of 52 cards, what is the probability that out of a hand of 5 cards you get 4 aces? Then the # of hands which has 4 aces is 48 (because the 5th card can be any of 48 other cards). So there is 1 chance in (2,598,960/48) = 54,145 of being dealt 4 aces in a 5 card hand.

How many 5 card poker hands can be dealt that contain 4 aces?

There is only 1 way to have the four Aces. The fifth card can be any of the remaining 48 cards. Hence, there are: 1 × 48 = 48 \displaystyle \,1\,\times\,48\:=\:48 1×48=48 hands that contain the four Aces.

What is the probability that a five card poker hand contains all the four aces?

What is the probability of getting a full house in poker?

3,473,184 2.60\%
Frequency of 7-card poker hands

Hand	Frequency	Probability
Full house	3,473,184	2.60\%
Flush (excluding royal flush and straight flush)	4,047,644	3.03\%
Straight (excluding royal flush and straight flush)	6,180,020	4.62\%
Three of a kind	6,461,620	4.83\%

What is the probability that a five card poker hand has no pairs?

Hands With No Pairs In stud poker, a pair refers to two cards of equal rank. There are four types of hands that do not have at least two cards of equal rank. That is, they do not have at least one pair.

What’s the probability that a 5 card poker hand for a standard deck of 52 cards contains exactly 3 or 4 Queens?

What is the probability of drawing an Ace 3 times in a row with replacement? This time, we are replacing the card, which means there will always be 4 Aces in the deck, and always 52 total cards.

What is the probability of all 5 cards from the same suit?

The probability is 0.003940. IF YOU MEAN TO EXCLUDE STRAIGHT FLUSHES AND ROYAL FLUSHES (SEE BELOW), the number of such hands is 10*[4-choose-1]^5 – 36 – 4 = 10200, with probability 0.00392465 A FLUSH Here all 5 cards are from the same suit (they may also be a straight). The number of such hands is (4-choose-1)* (13-choose-5).

How many hands can 5 cards form a straight in poker?

All 5 cards are from the same suit and they form a straight (they may also be a royal flush). The number of such hands is 4*10, and the probability is 0.0000153908. IF YOU MEAN TO EXCLUDE ROYAL FLUSHES, SUBTRACT 4 (SEE THE NEXT TYPE OF HAND): the number of hands would then be 4*10-4 = 36, with probability approximately

What is the probability of a straight flush in blackjack?

A STRAIGHT FLUSH All 5 cards are from the same suit and they form a straight (they may also be a royal flush). The number of such hands is 4*10, and the probability is 0.0000153908.

What is the probability of getting a hand in poker?

There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960.