A discrete random variable is a random variable that can only take on a countable number of values. This means that the possible outcomes of the variable can be listed out and the probabilities of each outcome can be calculated.

Examples of discrete random variables include:

- The number of heads obtained when flipping a coin 10 times
- The number of cars that pass through a toll booth in an hour
- The number of students who pass a test out of a group of 30
- The number of red balls drawn from a bag containing 10 red and 5 blue balls

To calculate the probabilities associated with a discrete random variable, one can use a probability distribution. This distribution lists out all the possible outcomes of the variable and their associated probabilities. The sum of all the probabilities in the distribution must equal 1.

For example, the probability distribution for the number of heads obtained when flipping a coin 10 times would look like this:

Number of Heads | Probability
----------------|------------
0 | 0.00098
1 | 0.00977
2 | 0.04395
3 | 0.11719
4 | 0.20508
5 | 0.24609
6 | 0.20508
7 | 0.11719
8 | 0.04395
9 | 0.00977
10 | 0.00098

This distribution shows the probability of obtaining each possible number of heads when flipping a coin 10 times. For example, the probability of getting exactly 5 heads is 0.24609.