Independent events are those situations where what happens in one event doesn't change what happens in another.

For example, think about flipping a coin and rolling a die.

The result of the coin flip—whether it lands on heads or tails—does not affect the number you roll on the die.

This idea is important when we use the multiplication rule in probability.

This rule says that for independent events, you can find the chance of both events happening by multiplying their individual chances.

Here’s how it works:

1. Identify the Events: Let's say Event A is flipping a coin (the chance of getting heads is (P(A) = \frac{1}{2})), and Event B is rolling a die and getting a 4 (the chance of getting a 4 is (P(B) = \frac{1}{6})).

2. Use the Multiplication Rule: Since these events don't affect each other, we can find the chance of both events happening together by using this formula:

   ( P(A \text{ and } B) = P(A) \times P(B) )

   So we have:

   ( P(A \text{ and } B) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} )

So, remember, when you deal with independent events, just use this simple multiplication method!