Find the probability of at most two accidents per day in total on these highways

Question

this is a question in my textbook that doesn't have a solution. Any help on an answer would be great.

There are three highways in the county. Independently from one another, the number of daily accidents that occur on these highways are Poisson random variables with respective parameters $.3$, $.5$, and $.7$.

Find the probability of at most two accidents per day in total on these highways.

My attempt:

let $X =$ number of accidents on each highway.

We want to find $P(X \leq 2) = P(X = 0, 1, 2) = P(X=0) +P(X= 1) + P(X=2)$

so $P(X=0) = (e^{-0.3})(e^{-0.5})(e^{-0.7})$

but I am having trouble finding $P(X = 1) $ and $P(X=2)$

Answer 1

Hint: $P(X=k)=\frac{(\lambda +\mu +\delta )^k}{k!}\cdot e^{-(\lambda +\mu +\delta)}$

$\lambda, \mu, \delta$ are the parameters. And k are the numbers of accidents in total on the three highways.