Statistics CH.5

Multiplication Rule for Independent Events

-The joint probability of any two independent events A and B: P( A and B)= P(A)*P(B)

Multiplication Rule

-used to calculate the joint probability of two events: P(A/B)= (P(A and B))/P(B) -The joint probability of any two events A and B: P(A and B)= P(B)*P(A/B) or P( A and B)= P(A)*P(B/A)

Requirement for probability:

1. The probability of any outcome must lie between 0 and 1. 2. The sum of the probabilities of all the outcomes in a sample space must be 1

Types of combination: 1. intersection of two events 2. union

1. the intersection of events A and B is the event that occurs when both A and B occur. (A and B) 2. the union of events A and B is the event that occurs when either A or B or both occur (A or B)

Additional Rule for Mutually Exclusive Events

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

Marginal probability

P(A1 and B1) + P(A1 and B2)

Complement Rule

P(A^c)= 1 - P(A) for any event A

Independent events

Two events A and B are said to be independent if: P(A/B)= P(A) or P(B/A)= P(B) -two events are independent if the probability of one event is not affected by the occurrence of the other event.

exhaustive

all possible outcomes must be included 1 2 3 4 5

simple event

an individual outcome of a sample space

subjective approach

define probability as the degree of belief that we would will hold in the occurrence of an event OPINIONS

relative frequency approach

defines probability as the long-run relative frequency with which an outcomes occurs (history of outcomes) LONG RUN

classic approach

determine probability associated with games of chance MATH

Additional Rule

enables to calculate the probability of the union of two events: P( A or B)= P(A) + P(B) - P(A and B)

event

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

sample space (S)

is a list of all possible outcomes of the experiment. A list of exhaustive and mutually exclusive outcomes O1, O2,....,O(k)

random experiment

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

mutually exclusive

no two outcomes can not occur at the same

Conditional Probability

the probability of one event given the occurrence of another related event. The probability of event A given event B: P(A/B)= P(A and B)/P(B) The probability of event B given event A: P(B/A)= P(A and B)/P(A)

The joint probability

the probability of the intersection

probability of an event

the sum of the probabilities of the simple events that constitute the event