When learning about probability, students often make some common mistakes. Here are a few of them to keep in mind:

1. Ignoring Sample Spaces: It's really important to define your sample space. This means you should clearly list out all the possible outcomes. If you skip this step, you might count things wrong, which can mess up your probability calculations.

2. Confusing Events: Sometimes, it's easy to mix up different types of events. Remember, independent events don't affect each other. On the other hand, dependent events are linked together and do influence each other.

3. Misusing the Addition Rule: Be careful with the addition rule! Use it correctly for events that can’t happen at the same time, known as mutually exclusive events. You would write it like this: $P(A \cup B) = P(A) + P(B)$. For events that can happen at the same time, called non-exclusive events, the rule changes a bit: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.

4. Overlooking Multiplication Rules: For independent events, the multiplication rule is pretty straightforward: $P(A \cap B) = P(A) \cdot P(B)$. Just make sure you use it only when it applies.

By keeping these points in mind, you can really improve your understanding of probability!