Prop bet: probability of hitting a J, 7, or 2 on the flop
 

Sometimes I offer a prop bet that either a J, 7, or 2 will hit on the flop. My understanding is that the odds are about 2:1 in my favor, but I cannot figure out how to come up with the answer. I have read that with 12 outs the odds are 46.7% with 2 cards to come and 27.3% with one care to come, but I cannot figure out how it works when one has 12 outs and is betting that 1 out hits on the flop. Any ideas?

Re: Prop bet: probability of hitting a J, 7, or 2 on the flop
 

There are 40 cards that are not J, 7 or 2. So your chance of losing is:

(40/52) x (39/51) x (38/50) = 59,280 / 132,600 = 44.7%

55.3% of the time, at least one J, 7 or 2 shows up on the flop.

Re: Prop bet: probability of hitting a J, 7, or 2 on the flop
 

Thanks!