Lesson 8.7

Page 645-648

#1-29 (ODD), 33, 35, 41, 43, 47, 49, 53-57 (ODD)

Pick up the handout on the table.

Probability

Objective

Students will know how to find the probabilities of events and their complements.

Probability - is a number between 0 and 1 that indicates the likelihood the event will occur.

* An event that is certain to occur has a probability of 1.

* An event that cannot occur has a probability of 0.

Sample Space - the set of all possible outcomes.

Event - any subcollection of a sample space.

Compound Event - the union or intersection of two events.

If there are no outcomes in the intersection of A

and B, then A and B are mutually exclusive

events.

All the outcomes for either of two events A and B, form the union of A and B.

Only the outcomes shared by both A and B form the intersection of A and B.

Probability of Compound Events

If A and B are two events, then the probability of A or B is :

P A or B P A P B P A and B

If A and B are mutually exclusive, then the probability of A or B is :

P A or B P A P B

Dependent Events - the occurrence of one event affects the occurrence of the other.

The probability that B will occur given that A has occurred is called the conditional

probability of B given A.

P B A

Probability of Dependent Events

If A and B are dependent events, then the probability that both A and B occur is :

P A and B P A P B A

Independent Events - the occurrence of one event has no effect on the occurrence of the other event.

Probability of Independent Events

If A and B are independent events, then the probability that both A and B occur is :

P A and B P A P B

Complement - consists of all outcomes that are not in A.

Event A’

“A prime”

What is the probability that an event is certain to occur?

Probability of the Complement of an Event

The probability of the complement of A is P(A’) = 1 - P(A).