This isn't correct; what would be correct is:

*given* the (random) number

of floods in a decade, the number

of deadly floods is a binomial random variable of parameters

and

.

Then we can deduce the mean and variance of

from the mean and variance given

and the law of

:

and

(thanks to computations with the binomial and Poisson distribution), hence

OR: In fact, you can prove (or perhaps you already know) that

is a Poisson random variable of parameter

, so that the above is immediate. A possible proof uses generating functions... Otherwise, if you know Poisson processes, this is a standard property: if we extract points independently with probability

, we get another Poisson process with intensity

.