When you start learning about probability in AS-Level Mathematics, there are some basic ideas you need to know. Here’s a simple breakdown of what you should understand:

1. Sample Spaces:

This is just a fancy term for all the possible outcomes in an experiment.

For example, if you flip a coin, the sample space is {Heads, Tails}.

2. Events:

An event is a specific outcome or a group of outcomes.

For instance, if you get Heads when flipping a coin, that’s one event. We can represent this event with the letter $E$.

3. Basic Probability Formula:

To find out how likely an event $E$ is to happen, you can use this formula:

$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

In simple terms, it means you take the number of ways the event can happen and divide it by all the possible outcomes.

4. Addition Rule:

If you have two events, $A$ and $B$, that cannot happen at the same time (we call them mutually exclusive), the chance of either one happening is:

$P(A \cup B) = P(A) + P(B)$

This means you just add their individual chances together.

5. Multiplication Rule:

If you have two independent events, $A$ and $B$, which means one doesn’t affect the other, the chance that both happen is:

$P(A \cap B) = P(A) \cdot P(B)$

This means you multiply the probability of the first event by the second event’s probability.

By understanding these rules, you’ll have a strong base to tackle any probability questions that come your way!