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Ace and Jack
There are 12 face cards in a standard deck of 52 cards. The odds of the first card being a face card is 12/52. If the first card drawn is a face card then there are 11 face cards remaining in the deck of 51 cards. The odds of a second draw of a face card is then 11/51. If both the first two cards drawn were face cards then the deck has 10 face cards in 50 total card. The odds of the third card also being a face card is 10/50. The total probability is (12/52)*(11/51)*(10/50) = 0.009954751 or just under one percent of the time.
There are 20 odd card is a pack of playing cards. This is a math problem.
If you put the one card back in before trying it the second time, then the odds are slightly worse; otherwise, the odds are the same - it does not matter if you pull two cards at once or one card twice, subject to the noted limitation.
If you assume that the Ace is high, then the odds of drawing a card higher than a nine is a standard deck of 52 cards is 20 in 52, or 5 in 13, or about 0.3846. If you assume that the Ace is low, then the odds of drawing a card higher than a nine is a standard deck of 52 cards is 16 in 52, or 4 in 13, or about 0.3077.
Since half of the cards (26 of the 52) are a red card (hearts and diamonds) the odds are 1 in 2 (or 50%) that any given card will be red.
Unfortunately, the yarborough hand must be played. Even though you have no card higher than a nine, there is nothing in the Laws of Bridge that allows you to throw in your hand. Rather, the rare occurrence of a yarborough hand is an opportunity for a side bet, of which the traditional odds are 1000 to one. However, since you have no high cards, there is a good chance that your partner has a good hand. Do whatever you can to support your partner.
For a dingle card drawn at random, it is 1/4.
The odds of getting a royal flush in five card stud is the same as in any poker game with five cards involved, i.e. 649,740 to 1.
There are 4 aces in the deck the odds that the first card is an ace is 4/52 or 1/13. The odds the second card is an ace is 3/51 or 1/17 because there are only 3 aces and 51 cards left. The odds that both are aces are 1/13 times 1/17 which is 1/221.
The odds of being dealt AK in Texas Hold'em is computed as follows:The first card can be either an A or a K, a total of 8 possible cards out of 52 cards in the deck. So, the probability is 8/52 = .153846.If you get an A on your first card, there are 4 Ks; if you get a K on your first card, there are 4 As. So in either case, if you get an A or a K on your first cards, there are 4 possible cards out of the remaining 51 cards that will make the AK hand, which is a probability of 8/51 = .078431Now, multiply two probabilities and you have .0121.To convert from probabilities into odds, divide the probability by (1 - probability). So, .0121 / (1 - .0121) = about 82 to 1.
3/4