Nicole pulls a colored marble out of a bowl, choosing the marble at random. There are 120 marbles in the bowl, of which 60 are black, 38 are white, and the rest are red. What is the probability that she will pull a red marble, set it to the side, and then pull a black marble out of the bowl?

Answer 1

To find the probability of pulling a red marble first and then a black marble, we need to calculate the probability of each event separately and then multiply the probabilities.

Probability of pulling a red marble:
There are 120 marbles in total, with 60 black, 38 white, and the rest red. This means there are 120 - 60 - 38 = 22 red marbles.
So, the probability of pulling a red marble first is 22/120 = 11/60.

After pulling a red marble, there are now 119 marbles in the bowl, with 60 black, 38 white, and 21 red.
Probability of pulling a black marble second:
There are 60 black marbles out of 119 total marbles remaining.
So, the probability of pulling a black marble second is 60/119.

Now, to find the probability of both events happening together, we multiply the probabilities:
P(red, then black) = P(red) * P(black)
P(red, then black) = (11/60) * (60/119)
P(red, then black) = 11/119

Therefore, the probability that Nicole will pull a red marble first and then a black marble out of the bowl is 11/119.