Spam in a Half-Hour

Emails arrive at an inbox as a Poisson process with rate $10$ per hour. Independently of everything else, each arriving email is spam with probability $0.2$.

What is the probability that exactly 2 spam emails arrive during a given 30-minute window?

Recall $P(X = k) = e^{-\lambda}\lambda^{k}/k!$.

Useful values: $e^{-1} \approx 0.3679$, $\quad e^{-2} \approx 0.1353$, $\quad e^{-5} \approx 0.006738$.