What is a Single Event?
A single event is one outcome or a set of outcomes from a single experiment. For example, rolling a die once and getting an even number is a single event.
Types of Events:
| Event Type | Definition | Example |
|---|---|---|
| **Compound Event** | Two or more outcomes combined | Rolling an odd number (1,3,5) |
| **Impossible Event** | Cannot occur | Rolling a 7 |
| **Certain Event** | Will always occur | Rolling a number < 7 |
Basic Probability Formula:
\[
P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]
Key Properties:
- 0 ≤ P(E) ≤ 1 for any event E
- P(impossible event) = 0
- P(certain event) = 1
- Sum of probabilities of all elementary events = 1
Common Probability Problems:
| Experiment | Sample Space | Example Event |
|---|---|---|
| Rolling a die | {1,2,3,4,5,6} | Getting a number > 4 |
| Drawing a card | 52 cards | Drawing a heart |
| Spinning a spinner | Equal sections | Landing on red |