What Are the Odds of Hitting A, J, or 2 on the Flop in Poker?

[Offramp]

What is the probability of anyone one of "A, J, 2" showing up on the the 3 card flop. I am assuming the number of player is 10 or less. I am assuming the probability is the same if it's 1 or 10 players , right? This is what I've calculated. Please let me know if I am correct.

Prob of 1st card being A, J or 2 is 12/52 = 0.230
if 1st card is none of the above then,

Prob of 2nd card being A, J or 2 is 12/51 =0.235
if 2nd card is none of the about then..

Prob of 3rd card being A, J, 2 is 12/50= 0.240

I would then sum up the prob. which is 0.705 am I correct?

 

[HallsofIvy]

While the probability does NOT depend on how many players there are, it does depend on what information you have: in other words what cards you have been dealt before the flop.

Assuming that you were not dealt any "A", "J", or "2", then, yes, the probability the first card is "A", "J", or "2" is 12/52= 0.230 and the probability that it is NOT is 48/52.

The probability that the first card is NOT one of those and the second card IS would be 12/51 times 48/52= 0.217 (approx.). The probability, in this case, that the second card is NOT one of those would be 1-0.217= 0.783.

The probability that the first two cards are NOT one of those three but the third card is would be 12/50 times 0.783= 0.188.

The probability that exactly one of the three cards is one of "A", "J", "2" is 0.230+ 0.217+ 0.188= 0.635.

The probability that at least one of the three cards is "A", "J", "2" would be much more complicated to calculate.

 

[cristo]

Assuming that you were not dealt any "A", "J", or "2", then, yes, the probability the first card is "A", "J", or "2" is 12/52= 0.230 and the probability that it is NOT is 48/52.

I don't think that is quite right: since you've been dealt two cards, you know what two of those cards are. If you've not got one of A J 2, then the probability of A J or 2 being the first card on the flop is 12/50. (etc.. for the other cards of the flop.)

 

[Offramp]

assuming that the two cards dealt to the players are NOT KNOWN, then what is the probability that atleast one of the 3 cards on the flop is a A, J, 2?