Probabilities and Spam Mails

Let's say, I am receiving new e-mails with Poisson distribution of rate = 'L' (at average) , and probability of an e-mail being non-spam is 'p'. (Assume every event is independent.)

Now calculate, some interesting things:

... ( I am working on the calculations now, please wait for the results.)

1. Average time between two non-spam e-mails are : 1/(L * p). (Although, average time between receiving two e-mails is only 1/L )
   
2. I want to see at least 1 non-spam e-mail in my inbox with probability greater than %99. (Say 'n' is the number of unread e-mail in my inbox) Then I have to wait until n > (-2/log(1-p)) (log is base 10.)
   

For one of my e-mail accounts, I find out that L=4, p=0.05. (I am counting only my Inbox, not including Junk Mail Folder).

Which means, I receive an email every 15 min. and I receive a non-spam email every 5 hour. I have to check my inbox after receiving 90 mails in order to have at least one normal e-mail with probability >%99.

I may expand this list, by giving more "real numbers" but I think even this much is enough to show, the status of my inbox. (This is only for 1 account and I have incountably many e-mail accounts, for different purposes!)

My special thanks goes to all hardworking spammers...