Econ 310 Chapter 6

Complement

- The complement of event A is the event that occurs when event A does not occur. - P(A^c) = 1-P(A)

Probability of an Event

- The probability of an event is the sum of probabilities of the simple events that constitute the event.

Independence

- Trying to find of if two events are related. In particular, we would like to know whether they are independent events. o Two events are independent if the probability of one event is not affected by the occurrence of the other event. - P(A I B) = P(A) or vice versa

Relative Frequency Approach

- number of observations divided by the total. o (1000 kids in a course, 200 get an A. 200/1000 = 20% chance to get an A) o It is only an estimate; relative frequency approach defines probability as 'long run' relative frequency. o Always use this to interoperate things.

Sample Space

- of a random experiment is a list of all possible outcomes of the experiment. The outcomes must be exhaustive and mutually exclusive.

Subjective approach

- when it is not reasonable to use the classical approach and there is no history of the outcomes, we have no alternative but to employ the subjective approach. o In this approach we define probability as the degree of belief that we hold in the occurrence of an event.

Event

A collection or set of one or more simple events in a sample space

Addition Rule

Allows us to calculate the probability of the union of two events..

Simple Event

An individual outcome of a sample space

Marginal Probability

Calculated by adding across rows or down columns, are so named because they are calculated in the margins of tables.

Addition Rules for Mutually Exclusive Events

P(A or B) = P(A) + P(B)

Multiplication rule for independent events

P(A)P(B)

Union of Events A and B

The union of events A and B is the event that occurs when either A or B or both occur.

Multiplication Rule

Used to calculate the joint probability of two events. P(A and B) = P(B)P(A I B) P(A and B) = P(A)P(B I A)

Exhaustive

all possible outcomes must be included

Random Experiment

an action or process that leads to one of the several possible outcomes.

Mutually Exclusive

meaning that no two outcomes can occur at the same time

Intersection of Events A and B

o The intersection of events A and B is the event that occurs when both A and B occur. Denoted as A and B. The probability of the intersection is called the joint probability.

Requirements of Probabilities

o The probability of any outcome must lie between 0 and 1. o The sum of the probabilities of all the outcomes in a sample space must be 1.

Conditional probability

probability of an event (A), given that (B) has already occurred.

Classical Approach

used by mathematicians to help determine the probability associated with games of chance. (Dice = 1/6 chance for any number if equally balanced.)