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Q: What is the probability that a hand of 13 cards contains no hearts?
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Continue Learning about Math & Arithmetic

What is the probability in a regular 52 deck of getting a hand with no diamonds given that the cards are red?

The answer depends on how many cards are in the hand.


In a poker hand consisting of 5 cards find the probability of holding 3 aces?

Approximately 2%


How many ways can a hand of five cards consisting of four cards from one suit and one card from another suit be drawn from a standard deck of cards I think combination?

The probability of five cards being four cards from one suit and one card from another suit is the same as the probability of drawing four cards from one suit multiplied by the probability of drawing one card from another suit, multiplied by 5 (for each of the possible positions this other card can be drawn in). The probability of drawing four cards from one suit is 12/51 x 11/50 x 10/49. The probability of drawing a fifth card from another suit is 39/48. All these numbers multiplied together (and multiplied by 5) come to 0.0429. So the probability of drawing a hand of five cards with four cards from one suit and one card from another is 5.29%


WHAT IS the probability for getting a heart flush in a 5-card poker hand dealt from a complete shuffled deck of ordinary playing cards?

Total combinations for drawing 5 cards is 52 choose 5 which is...52*51*50*49*48/(5*4*3*2*1) possible outcomes for drawing 5 hearts is 13 choose 5 which is...13*12*11*10*9/(5*4*3*2*1) Probability of drawing 5 hearts is (52 choose 5)/(13 choose 5) which is....000495


What are the odds of hitting a royal flush in video poker holding a king of hearts and a jack of hearts and drawing three cards?

Since it's video poker, we can assume that the only cards drawn are the ones you started with. There are exactly 47 cards left in the deck. There are 6 series of draws you can get that will give you ace, queen, and 10 (3!, or 3x2x1).The number of sequences of 3 cards in a 47 card deck is 47!/44!, or 47x46x45, and since 6 of the sequences leave you with the hand you want, you have exactly 6/(47x46x45) probability to get one of them.This works out to 1 in 16,215.