Two events are independent if the occurrence of one does not change the probability of the other.

If \(A\) and \(B\) are independent, then:

So knowing that one event has happened gives no new information about the other.

For independent events \(A\) and \(B\):

We multiply the probabilities because the events do not affect each other.

A fair coin is tossed and a fair die is rolled.

Let:

• \(A\): getting heads
• \(B\): getting a 6

These events are independent.

\[ P(A)=\frac{1}{2}, \qquad P(B)=\frac{1}{6} \]

So:

Two events \(A\) and \(B\) are independent if and only if:

If this equality is not true, then the events are not independent.