Sample spaces are really important for understanding compound events in probability, especially for Year 9 students. A sample space shows all the possible results of an experiment. This helps us figure out the chances of different events happening.

Key Points:

1. What is a Sample Space?

   • A sample space, which we call $S$, is all the possible outcomes. For example, when you flip a coin, the sample space is $S = \{H, T\}$, which means you can get either heads (H) or tails (T).

2. What are Compound Events?

   • Compound events are made up of two or more simple events. For example, if you roll a die and flip a coin, you can get results like $(1, H)$ or $(6, T)$. In this case, your sample space has 12 different outcomes.

3. How to Calculate Probabilities?

   • To find the probability of a compound event, you can count the number of good outcomes and divide it by the total number of outcomes. For example, if you want to know the probability of rolling a 3 or flipping heads, you can use the formula:
     $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.

4. Why is This Important?

   • Knowing about sample spaces helps students understand and calculate probabilities better. This skill improves their problem-solving abilities in statistics. Learning about different combinations of events can also help them make better choices in real life.