License plate method example:
Find the number of possible combinations for a license plate in the format:
I know that using
C(13,2)[...]/C(52,5) is the appropriate way of determining the probability of a full house. I found a strange outcome using the license plate method though, so please humor me.
The license plate method I used, which assumes the probability of a full house is equal to the probability of a pair * the probability of three of a kind.
[1 * (3/51)] * [1 * (3/50) * (2/49)]
Deal one card. To create a pair, the next card must be one of the 3 remaining with the same denomination.
Deal another card. To create three of a kind, the next card must be one of the remaining 3 with the same denomination, and the final card must be one of the remaining 2 with the same denomination.
The correct answer: (3744/2598960) =
My incorrect license plate method result is exactly one order of magnitude less than the correct answer. It's actually 10x more likely to get a full house.
- Is it possible to calculate the probability of a full house using the license plate method, and if so, how?
- Is the results being off by exactly an order of magnitude a coincidence, and if not what is the correlation?
Assumptions: 52 card deck, 13 denominations, 4 suits