Hi everyone,

I joined the forum just to ask this question about one issue I'm having with probability. Your help is much appreciated. I already have my bachelors in math (graduated five years ago) and have just started studying probability independently in order to prepare for the first actuarial exam (not 100% it's for me. Figured I'd start studying and see how it goes). I'm getting the concepts so far, though maybe not as quickly as I would have liked, but one question has me stumped!

So the question is basically, for all equally likely five card poker hands, what is the probabiiity of having a one pair?

I did it wrong the first time.

The way I solved it originally was, I multiplied 52*3*48*44*40, to get the number of ORDERED poker hands with a one pair, then divided by 5! to get the number of unordered poker hands. Then I divided by ( 52 over 5 ) [sorry, I've never posted a question like this online before and don't know how to the binomial notation properly on the forum] to get the probability. The answer this gives is .04226.

Turns out the answer is actually .4226 and I figured out how to get that, but WHY did my original method not work and WHY was the answer off by exactly a factor of 10? I am really stumped. I haven't been studying for even a week, and so far I have been able to eventuallly answer all my own questions, but I really can't figure this one out, and I bet if I knew why my original answer didn't work, it would help me better understand the concepts.

Thanks so much for your help! I eagerly await an answer!