Calculating the chance of a simple event is an important part of learning about probability.

Let's start by understanding what a "simple event" means.

A simple event is when there is just one outcome.

Steps to Calculate Probability

1. Identify the Experiment: First, figure out what the experiment is. For example, if you roll a six-sided die, then the experiment is rolling that die.

2. Define the Sample Space: The sample space is all the possible outcomes from your experiment. For a six-sided die, the sample space $S$ is: $S = \{1, 2, 3, 4, 5, 6\}$

3. Count the Total Outcomes: In this case, there are 6 possible outcomes (the numbers 1 through 6).

4. Count the Favorable Outcomes: Next, find out the specific outcome you want. If you are looking for the chance of rolling a 4, there is only 1 favorable outcome (the number 4).

5. Use the Probability Formula: The formula for probability $P$ of a simple event is: $P(E) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}$

   So in our example: $P(\text{rolling a 4}) = \frac{1}{6}$

Example

Now, let’s look at another example. Imagine you are drawing a card from a regular deck of 52 playing cards.

• The sample space here has 52 outcomes.

• If you want to find the probability of drawing an Ace, there are 4 favorable outcomes (the four Aces).

Using the formula: $P(\text{drawing an Ace}) = \frac{4}{52} = \frac{1}{13}$

Conclusion

Calculating the probability of a simple event is easy when you follow these steps.

Practice with different situations, and you will get better at these ideas!