Problem: 100 Cars are going to be randomly assigned to inspection team A or inspection team B (but not both). They are assigned to team A with probability

and team B with probability

Team A randomly passes cars with probability

and Team B randomly passes cars with probability

How many cars do you expect to pass inspection?

I'm not sure how easy this is. Here's what I did:

I would expect 100(.6)=60 cars to go to Team A and 40 cars to go to team B.

Then of the 60 Team A inspects, 60(.35)=21 should pass

Of the 40 Team B inspects, 40(.6)=24 should pass

So I would expect 21+24=45 to pass?

Is this alright?