What Are the Odds of Drawing at Least One King, Queen, or Ace in Three Attempts?

[clarkd25]

In a 52 card deck if you choose 3 random cards such as any King any queen or any ace
(12 cards in total) what is the probability of being able to draw at least one of these cards with 3 attempts and not replacing a drawn card. Basically my question is regarding the odds in Texas Holdem of choosing 3 random cards and flopping at least one of them. It seems to me that on the first card the odds of success are 12/52 and then on the second draw if not successful would be 12/51 and then 12/50, but I just don't think I know how to do the math for the problem. Please Help.

 

[clarkd25]

Duh!

I went about solving the problem the wrong way. Instead of trying to figure out the probability of flopping at least one of the cards I should have solved for the probability of flopping none of the cards which would be (40/52)*(39/51)*(38/50) which results in 44.7%. This would mean that the probability of flopping at least one of my randomly selected cards woul be 55.3%. My reason for figuring out this problem is that I like to make prop bets when I play poker and wanted to know if this was a good even money bet for me to select 3 cards and betting that one of them would come on the flop. By having chance greater than 50% of hitting one of my cards this bet has a +EV.

 

[tacman]

The probability of drawing at least one of the desired cards with 3 attempts and not replacing a drawn card can be calculated using the formula for combinations.

First, we need to find the total number of possible combinations of 3 cards from a deck of 52 cards. This can be calculated as 52C3 = 52! / (3! * (52-3)!) = 22,100.

Next, we need to find the number of combinations that include at least one of the desired cards. This can be calculated as 12C1 * 39C2 = 12 * 741 = 8,892.

Therefore, the probability of drawing at least one of the desired cards with 3 attempts and not replacing a drawn card is 8,892 / 22,100 = 0.4026, or approximately 40.26%.

In Texas Holdem, the odds of choosing 3 random cards and flopping at least one of them would be slightly different as there are already 3 community cards on the table. However, using the same formula, the probability would be higher as there are fewer unknown cards in the deck.