# Independent Events

## Independent Events

Events for which the occurrence or non-occurrence of one does not affect the probability of the occurrence of the other.

An event whose occurrence does not depend on the result of another event is sometimes called a simple event.

### Property

The probability that two independent events will occur in the same random experiment is equal to the product of their probabilities.
Therefore, if A and B are events in a probability space U, we have the equation: P(A) × P(B) = P(A ∩ B)

### Example

Consider experiment A, which consists of rolling an honest die with six faces numbered 1 to 6, and experiment B, which consists of drawing one card from a deck of 8 cards (aces and kings). These two events do not have any connection to one another and the occurrence of one does not influence the occurrence of the other.

The probability of A and B is: P(A) × P(B) = $$\frac{1}{6}$$ × $$\frac{1}{8}$$ = $$\frac{1}{48}$$.