Understanding Probability with Simple Examples

In probability, we can create complex events from simple outcomes. Let’s break this down using a common example: rolling a die.

1. Simple Outcome: When you roll a die, you can get one of six numbers: {1, 2, 3, 4, 5, 6}.

2. Sample Space: This is just a fancy term for all the possible outcomes. For one die, the sample space is:

   • $S = \{1, 2, 3, 4, 5, 6\}$.

3. Complex Event Example: Now, let’s look at a more complicated event. For instance, the event "rolling an even number" comes from the simple outcomes {2, 4, 6}.

4. Probability Calculation:

   • To find the chance of rolling an even number, we can use this formula:

   $P(\text{Even}) = \frac{\text{Number of good outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}$

This means you have a 50% chance of rolling an even number!

So, we see how we can take simple outcomes and mix them together to form more complex events, and then figure out their probabilities.