# MA375: Lecture Notes

Fall 2008, Prof. Walther

## Some Definitions

If **E** and **F** are events in **S** (sample space) the the conditional probability of **E** and **F** is **P(E|F) = P(E intersect F)**.

Further :

```
the conditional probability of "E" given "F" is =$ \frac {P(EnF)}{P(F)} $
```

*defn:* if P(E|F) = P(E) , then E and F are independent events otherwise they are dependant events.

```
note: independence implies that $ P(E)= P(E|F) = \frac {P(EnF)}{P(F)} $
or P(E).P(F)=P(EnF).
note : if P(E|F) = P(E)
then P(F|E) = P(F)
```