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A random variable is an essential concept in statistics and probability. It helps us model situations where outcomes are determined by chance. A random variable can take on different values, each with a certain probability.
There are two main types of random variables: discrete and continuous. Discrete random variables have a finite or countable number of potential outcomes. For example, tossing a coin results in either heads or tails. In the given problem, we looked at whether a student took the SAT. Here, the outcome is binary—either they did, or they didn't. This makes it a discrete random variable.
On the other hand, continuous random variables can take on an infinite number of values within a given range. Think of measuring the exact weight of a bag of apples. In our exercise, the SAT scores of students were considered as a random variable. Since SAT scores can range from 0 to 2400, with countless possible scores, this is more like a continuous variable. However, because they don't fit the criteria of a binomial distribution, they are examined differently in statistics.

Probability measures how likely an event is to occur. It ranges from 0 (impossible event) to 1 (certain event). Mathmatically, it's the ratio of the number of ways an event can occur to the total number of possible outcomes.
If you have a fair coin, the probability of getting heads in one toss is 0.5, because there are two possible outcomes, heads or tails, and only one of them is heads.
In the exercise, the probability of a student taking the SAT was given as 0.45, or 45%. This probability was used to model the binomial distribution, showing the chance of a student, randomly chosen from the whole group, to take the SAT.
Understanding probability is crucial to predict how often an event is likely to happen. In real-life scenarios, it helps make decisions based on the likelihood of various outcomes.

The SAT is a standardized test widely used for college admissions in the United States. Comprising three main sections—Reading, Math, and Writing—the scores can help colleges evaluate a student's readiness for academic success.
The test scores of SAT are issued on a range from 400 to 1600, combining the three sections. With each section scored between 200 and 800. In our exercise, the average SAT score was used to demonstrate concepts in probability and random variables.
For probabilities surrounding SAT scores, the random variable of interest was the number of students taking the test, since the problem dealt with a binary outcome: taken or not taken. Consequently, individual scores didn’t fit the binomial distribution because scores vary widely, representing continuous outcomes, not the discrete, all-or-nothing results needed for binomial modeling.