## 13.3 Outline

- Complementary probabilities
- symbols
- property of complements

- Odds
- in favor
- against
- find odds, given the probability
- find probability, given the odds

- Conditional probability
- definition
- formula
- procedure for using tree diagrams

## 13.3 Essential Ideas

PROPERTY OF COMPLEMENTS:

*P*(*E*) = 1 – *P*(*E *compliment)

**Odds in favor** of an event *E *:

*s/f *(ratio of good to bad)

**Odds against **an event *E *:

*f/s* (ratio of bad to good)

*s = *NUMBER OF SUCCESSES

*f* = NUMBER OF POSSIBILITIES

*s + f = n*

*
*Suppose that you

*know*(

**P***E*) and wish to find the odds:

*odds in favor *of an event *E *:

*P*(*E *)/*P*(*E *compliment)

*odd against* on event *E *:

*P*(*E *compliment)/*P*(*E *)

Suppose that you *know* the odds in favor of an event *E* and wish to find the probability:

*P*(*E *) = *s/*(*s + f*)

and

*P*(*E* compliment) = *f/*(s + *f*)

The **fundamental counting principle **gives the number of ways of two or more tasks. If task *A *can be performed in *m* ways, and if, after task *A* is performed, a second task *B*, can be performed in *n *ways, then task *A* followed by task *B* can be performed in *mn* ways.

The probability of an event *E* given that another event *F* has occurred is called a **conditional probability**, and is denoted by *P*(*E | F*).

The procedure for using tree diagrams:

Multiply when moving horizontally across a limb.

Add when moving vertically from limb to limb.

Conditional probabilities; start at their condition.

Unconditional probabilities; start at the beginning of the tree.