Binomial and Poisson Distribution.

Hi, I understand both the poisson distribution and binomial distribution relatively well. However, the way I see it, for any question requiring the use of a poisson distribution, it makes sense that a binomial distribution could be used. For example:

"A hockey team has a shut out at a rate of 1 of every 20 games. calculate the probability of having 2 shutouts in the next 10 games."

The reason I believe binomial applies is: the probability of success is 0.05%, the number of trials is 10, and the desired number of shutouts is 2.