Question 1183307
The number of possible passwords is 36^6=2176782336
With a billion password attempts the mean number of passwords one would get with the same probability each time (it is with replacement) is 1 billion/the above probability
That equals 0.4594 hits, n*p.
When n goes to infinity and p goes to 0 (but is not 0), the binomial distribution, which this is, can be approximated by a Poisson, where np=lambda.  Dist is Bin~(1,000,000,000, 1 /36^6)
p(0)=e^(-0.4594)*0.4594^0/0!=0.6317
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The mean and the variance are equal in a Poisson distribution, and they are 0.4594 hits/hits^2 respectively.