A bag contains 8 black marbles and 20 yellow marbles.
You reach into the bag and pull out a black marble.
Then you reach into the bag and pull out another marble.
What is the probability that the second marble is yellow?
20/27
To find the probability of pulling a yellow marble after pulling a black marble, we need to consider the total number of marbles and the number of yellow marbles remaining in the bag.
Step 1: Calculate the probability of pulling a black marble first.
In the bag, there are a total of 8 black marbles and 20 yellow marbles, making a total of 8 + 20 = 28 marbles. Therefore, the probability of pulling a black marble first is 8/28 = 2/7.
Step 2: Calculate the probability of pulling a yellow marble as the second marble, given that the first marble was black.
After removing one black marble from the bag, there will be a total of 27 marbles left. Out of these, 20 are yellow marbles. So, the probability of pulling a yellow marble as the second marble, given that the first marble was black, is 20/27.
Step 3: Multiply the probabilities from steps 1 and 2.
To find the probability of both events occurring, we multiply the probability of pulling a black marble first (2/7) and the probability of pulling a yellow marble as the second marble (20/27).
(2/7) * (20/27) = 40/189
Therefore, the probability of pulling a yellow marble as the second marble, after pulling a black marble first, is 40/189.