Independent Events

Tow events A and B are statisitically independent if neither influences the oother. The probability of event A occurring does not influence the probability of event B occurring and vice verse.

Suppose neither event A or event B has occurred yet. Event A then occurs – or it doesn't. The probability of event B may or may not change but it will not change because event A occurred – or didn't. The same may be said about the influence of event B on event A occurring.

When events A and B are independent like this, we may write down some equations relating the probabilities of events A or B occurring or not.

Events A and B both occur

Neither events A or B occur

Event A occurs but B does not

Event A does not occur but B does

We may also condider 'conditional probability'. Given that event A has happened, what is the probability that B will happen?

The probability of event A happening given that B has already happened is writtenand is calculated from

Since A and B are independent,so