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What is the probability that a random selected poker hand contains exactly 3 aces given that it contains at least 2 aces?
To calculate the probability of a random selected poker hand containing exactly 3 aces given that it contains at least 2 aces, we first need to determine the total number of ways to choose a poker hand with at least 2 aces. This can be done by considering the different combinations of choosing 2, 3, or 4 aces from the 4 available in a standard deck of 52 cards. Once we have the total number of ways to choose at least 2 aces, we then calculate the number of ways to choose exactly 3 aces from the selected hand. Finally, we divide the number of ways to choose exactly 3 aces by the total number of ways to choose at least 2 aces to obtain the probability.
The probability of being dealt 4 aces in a 5 card poker hand?
Poker hands are combinations of cards (when the order does not matter, but each object can be chosen only once.)The number 52C5 of combinations of 52 cards taken 5 at a time is (52x51x50x49x48) / (5x4x3x2x1) = 2,598,960.The number of hands which contain 4 aces is 48 (the fifth 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.The odds are 54,144 to 1 against. The probabilityis 1/54145 = (approx.) 0.000018469 or 0.0018469%.
A deck of ordinary cards is shuffled and 13 cards are dealt. What is the probability that the last card dealt is an ace?
The odds of any card pulled from an ordinary deck of 52 cards being an Ace is 4 in 52 (4 aces in a deck of 52). This can be reduced to a 1 in 13 chance of any random card pulled from the deck being an Ace (or any other specific value, for that matter). That 13th last card dealt in a hand is no different than picking a random card out of the pack, regardless of what cards you deal before (face down or blindfolded or even face up, it doesn't matter). A more interesting question would be "what would the probability be of ANY of those 13 cards being an Ace?" Any takers?
What is the probability of getting exactly three aces in a five-card poker hand dealt from an ordinary 52 card deck?
The probability of getting 3 aces in the order AAABB is; P(AAABB) = (4/52)∙(3/51)∙(2/50)∙(48/49)∙(47/48) = 0.0001736... There are 5C3 = 5!/(3!∙(5-3)!) = 10 different ways in which the aces can come out. So the probability of getting exactly three aces in a five card poker hand dealt from a 52 card deck is, P(3A) ~ 10∙(0.0001736) ~ 0.001736 ~ 0.1736%
What is the probability of not being dealt a queen in a 52 card deck?
The answer will depend on the exact situation.If you are dealt a single card, the probability of that single card not being a queen is 12/13 - assuming you have no knowledge about the other cards.Here is another example. If you already hold three queens in your hand (and no other cards have been dealt), the probability of the next card being dealt being a queen is 1/49, so the probability of NOT getting a queen is 48/49 - higher than in the previous example.
