A bag contains 10 marbles, and 4 of the marbles are black. Joseph chooses 2 marbles at random without replacing the first marble. What is the probability that both marbles are black?

Question

SmokeyBrown · Answer

It's a bit of a complex problem, but it becomes simpler if you think of choosing the marbles one at a time.
For the first marble, there are 4 black marbles out of 10 total marbles, so the chance of choosing a black marble is 4/10.
Then, for the second marble, remember that we do *not* replace the first marble. So, there would be 9 marbles left in the bag, and 3 of these would be black. So, the chance of choosing a second black marble is 3/9.
Finally, to calculate the probability of both of these events happening, just multiply the probability of both events together.
(4/10)*(3/9)=?