Start by finding the probability that c is not called, given that there are n bugs.

P(C' | n) = 0.9^n

Now, the required probability is:

P(n=0) * 1

+P(n=1)*0.9

+P(n=2)*0.9^2

...

We are told the distribution of N.

So the sum you want to do is

You are supposed to recognise the above as

where Y is a poisson(2.7) variable.

So the answer is