Events are important when we talk about probability because they help us understand how likely different things are to happen. An event is basically one specific result or a group of results from a random experiment. This helps us figure out the chances of different outcomes.

Key Ideas:

• Sample Space (S): This is the list of all the possible outcomes. For example, if you flip a coin, the sample space is $S = \{ \text{Heads, Tails} \}$.

• Events: These are part of the sample space. For example, if you want to find out the chance of getting Heads when you flip a coin, that event would be $E = \{ \text{Heads} \}$.

How to Calculate Probability:

To figure out the probability of an event $E$, we can use this formula:

$P(E) = \frac{|E|}{|S|}$

In this formula, $|E|$ is the number of outcomes that are good for event $E$, and $|S|$ is the total number of outcomes in the sample space.

Example:

Let’s look at rolling a six-sided die:

• The Sample Space is: $S = \{1, 2, 3, 4, 5, 6\}$. So, $|S| = 6$.

• If we want to find out the event of rolling an even number, we have: $E = \{2, 4, 6\}$, which means $|E| = 3$.

Now, we can calculate the probability:

$P(E) = \frac{3}{6} = \frac{1}{2} = 0.5$

This tells us that there is a 50% chance of rolling an even number.

By understanding events, we can better understand uncertainty and how likely different things are to happen in probability.