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 written
and is calculated from
Since A and B are independent,so
Similarly,
