Titled link: BART's new train cars now in service | bart.gov
-- apparently the 10 that have been used for tests. Another 10 are currently being tested, and production should go up to some 16 - 20 cars per month. BART has currently ordered 775 cars and it is seeking funding for an additional 306 cars for Silicon-Valley service.
I will now estimate how well those 10 cars can hold down initial service: Richmond - Warm Springs on weeknights and weekends. The one-way travel time is 1h 8m and 1h 9m, making 2h 17m total. The trains run once every 20 minutes, making 7 trains necessary. If the 10 cars are split onto 5 2-car trains, then that will almost but not quite be enough. If they are split as 3 - 2 - 2 - 3 or 3 - 4 - 3, then roughly one out of every two trains will have the new railcars.