# Statistics Examples

, ,

Step 1

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

Step 2

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

Step 3

Step 3.1

Using the Bayes' rule, .

Step 3.2

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

Step 3.3

Cancel the common factor of .

Step 3.3.1

Cancel the common factor.

Step 3.3.2

Divide by .

Step 4

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

Step 5

and , which means that and are independent events.

A and B are independent events