Hi all, hope you are having a fine day

My problem is:

Let X and Y be independent Poisson distributed stochastic variables, with expectation values

5 and 10, respectively. Calculate the following probabilities:

X + Y > 10

What I have done to solve it:

I found the Poisson probabilities when r = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 for both X and Y, then I added them all together, and subtracted them from 1. I keep getting the wrong answer, and my answer is over 1, which is a bit strange. The answer key says the correct answer should be: 0,882

Thanks!