A bag contains 10 red marbles, 5 gray marbles, 12 black marbles, and 8 white marbles. Two marbles are randomly drawn from the bag without replacement. What is the probability of drawing a black marble followed by a red marble?

This is conditional probability because you are not replacing the marble. That means on the second pick you'll have one less marble and you want to multiply your fractions together not add them, so ...

first event 12/35 times second event 10/34

12/119