Probability of independent events within a specified window So I have an event that can occur on a daily basis with probabilty 1%. There is no dependence between days. Now I can calculate the probabality of the event occuring X times in Y days:
  COMBIN(Y,X) * (0.01 ^ X) * [0.99 ^ (Y - X)]

where COMBIN() is the number of combinations for X in Y. Now what I'd like to calculate is the probablity of X events in any Y window for the last Z days, e.g what is the probability of 5 events occuring in at least one 30 day window during the last 10 years. Any assistance much appreciated.
Thanks  
Note: Original question edited to add "at least" qualifier per MansT suggestion below.
 A: If the days are truly independent as you say then let us denote an event A as X events in any Y day period and denote P(A), the probability of X events in Y days:
P(A) = COMBIN(Y,X) * (0.01 ^ X) * [0.99 ^ (Y - X)]
This is true for any Y day window provided the probability of an event occurring is not time dependent.
Then you can apply the Binomial probability again to the event A.  We have to be careful because now the event A is not independent for overlapping windows, i.e. for a window of length 10, the probability of event A on days 1-10 is not independent of days 2-11.  Thus the following is assuming non-overlapping windows to ensure independence.  Now,  because you want the probability of at least one non-overlapping window having an event, it is easier to do:
1 - P(no overlapping windows satisfying event A).
Let n be the number of non-overlapping windows of size Y in time period Z.  Then the probability of X events in a non-overlapping window of size Y over a time period Z is:

1 - COMBIN(n,0) * P(A)^0 * [1-P(A)]^(Y-0)
= 1 - n * [1-P(A)]^Y

