There are 5 white, 3 black, and 2 red marbles in a bag. What is the probability of drawing a black marble?

In order to find the probability of drawing a black marble, we need to first determine the total number of marbles in the bag and then find the number of desired outcomes (i.e., the number of black marbles).

Let’s denote the total number of marbles as n(S), where S is our sample space. We compute the total number of marbles in the bag:

n(S) = 5(white marbles) + 3(black[marbles) + 2(red marbles) = 10

Now let’s denote the number of black marbles as n(B), which is 3.

To find the probability of drawing a black marble, we can use the formula:

$$P(B) = \frac{n(B)}{n(S)}$$

Now, we can plug in the values we found earlier into this formula:

$$P(B) = \frac{3}{10}$$

So, the probability of drawing a black marble from the bag is $\frac{3}{10}$, or 30%.