[Alchemist]

I made a post similar to this in the Probability forum but it didn't get any responses so I'll give it a shot here.

I'm trying to come up with a general formula to do this:

Suppose you play 200 hands in a session. Let's say you're dealt at least one Nine in 55 of your starting hands. What's the likelihood of that and how many SD is that from the norm?

About as far as I've gotten was the probability of getting dealt at least one Nine:
1-[(48/52)(47/51)(46/50)] ~= 0.21738

Would it be correct to say that the expected number of starting hands with a Nine would be: p*H ? In this case: 0.21735 * 200 = 43.5? Then what?