# Statistics Examples

, ,

Two events are independent events when the occurrence of one does not affect the probability of the other. and .

should equal to because the occurrence of should not effect the probability of for independent events and . In this case, .

Using the Bayes' rule, .

Substitute the given values , , and in Bayes' rule.

Simplify .

Remove parentheses.

Multiply by .

Multiply by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

should equal to because the occurrence of should not effect the probability of for independent events and . In this case, .

and , which means that and are independent events.

A and B are independent events