Compound events are important in probability because they mix two or more simple events. This changes how we think about results and how we do our calculations.

Definitions

• Simple Event: This is when something happens with one possible outcome. For example, rolling a die and getting a 4.
• Compound Event: This is when we put together two or more simple events. For example, rolling a die and getting an odd number.

Types of Compound Events

1. Independent Events: This happens when one event doesn’t change the outcome of another event. For example, flipping a coin and rolling a die at the same time.

2. Dependent Events: In this case, one event affects the other. For example, if you draw cards from a deck without putting any back, the outcome of the first draw affects the next one.

Probability Calculation

• For independent events, to find the chance of both events happening, we use this formula: $P(A \text{ and } B) = P(A) \times P(B)$

• For dependent events, we change the formula a bit to account for what happened before: $P(A \text{ and } B) = P(A) \times P(B|A)$

Impact on Outcomes

Knowing about compound events helps us understand more complicated probability problems. This skill is very useful in real life.

For example, if two dice are rolled, the chance of getting a total of 7 is $P(7) = \frac{6}{36} = \frac{1}{6}$.