Best way to get a feel for this is to play around with a binomial calculator.
http://www.stat.sc.edu/~west/applets/binomialdemo.html (java applet with graph)
http://www.swogstat.org/stat/public/...calculator.htm (non java)
N is number of trials, p is probability (for AA, p = 1/221 ~= 0.00452, for AA-JJ, p ~=0.0181). Then enter different values for X or t and see how likely different frequencies are. Use the "at least" or "more than" functions to see how many lie above and below that number.
For example, using the java based calculator above with N=1000, p = 0.0045, X = 0, the probability that you will get zero AA out of N = 1000 hands is 1.1%. The probability of getting more than 7 is 8.6%