To figure out the chance of simple events, we need to know three important things: events, sample spaces, and outcomes. Let’s break these down.

Definitions:

• Event: This is a specific result or a group of results from an activity. For example, when you roll a die and get a 4.

• Sample Space: This is all the possible results of an activity. If you roll a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.

• Outcome: This is just one result of an event.

Probability Formula:

To calculate the probability ( P ) of a simple event, you can use this formula:

[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes in the sample space}} ]

Example:

Let’s look at an example with a six-sided die. We want to find the chance of rolling an even number (which are 2, 4, or 6).

1. Identify the Sample Space: For a die, the sample space is {1, 2, 3, 4, 5, 6}.

2. Count the Total Outcomes: There are 6 possible outcomes when you roll the die.

3. Identify Favorable Outcomes: The even numbers we can roll are {2, 4, 6}. So, there are 3 favorable outcomes.

4. Apply the Probability Formula:

[ P(\text{even number}) = \frac{3}{6} = \frac{1}{2} \approx 0.5 ]

Conclusion:

So, the chance of rolling an even number on a six-sided die is 0.5. This means there’s a 50% chance that you’ll roll an even number. Learning how to calculate these chances is important when studying probability in math.