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When we have an event, that his occurence doesn't affect the other, it is called independent.
If A and B are independent, than:
P(A|B)=P(A) AND P(B|A)=P(B)
In this case the multiplicative rule of probability may be:
P(A∩B)=P(A)*P(B)

So, independent is when the occurence of event A doesn't affect the accurence of B, that might even occur;
And mutually exclusive is when the occurence of A happens, B cannot happen.

Poisson distribuition need some mathematical rules to be applied:
1. The probability of an event occur is proportional to the lengh of the interval and an infineite number is possible (x! - x factorial)
2. Events occur independently of a rate lambda (λ).

The λ is a parameter that represents the mean and the variance, n gets huge, p gets tiny.
mean = λ = np
variance = λ = np (1-p)

We use the Possoin model when the variance goes up with the mean (skewed distribuition).

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