A compound event is an event that is expressed in terms of other events. For example given events A and B, compound statements would be both events A and B occurring together or either event A or B occurring or neither A nor B occurring.

1. Know how to draw and interpret a Venn diagram.

A Venn diagram is a graphical representation of events and their sample space.

For two events: event A, event B, the sample space can be represented by S or U where U means the universe of all possible outcome.

A Venn diagram of two events A and B in which the shaped region indicates the events. Note that the two events do not overlap in this Venn diagram. This is call a mutually exclusive events.
 

2. Know how to calculate the probability of compound events.

These are the various types of compound events and their appropriate probability rules and Venn diagrams.

Mutually Exclusive Events (events cannot occur together - shaped Area)
 

Venn Diagram - Mutually Exclusive Events	Rule:Addition Rule: If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)
Definition: Events A and B are mutually exclusive if the occurrence of one precludes the other, so that both A and B happening at the same time is impossible. Example: The probability of getting both a King and Queen in selecting just one playing cards from a deck of cards is an impossible event.	Rule Example: What is the probability of getting a 2 or a 3 from the roll of a single die? P(2 or 3) = P(2) + P(3) =

A or B (either event A or B occurring) -Union or  (shaped Area)
 

Venn Diagram - Union of A or B	Mutually Exclusive Events - Addition Rule: Prob (A or B) P(A or B) = P(A) + P(B) Same as mutually exclusive When not Mutually Exclusive Events: P(A or B) = P(A) + P(B) - P(A and B)
Definition: Union: (A or B) - Events A or B occurring if either A occurs or B occurs or both occur. Example: The probability of getting either a Queen or Heart. Number of Queens = 4, Sample space = 52 Number of Hearts = 13 Number of Queens and Hearts = 1	Rule Example: What is the probability of getting a Queen or a Heart from selecting a card from a deck of cards? Related Events: P(Queen or Heart) = P(Queen)+P(Heart)-P(Queen and Heart) P(Queen or Hearts) =  Mutually Exclusive Events: The probability of getting a King or Queen - Pr[K or Q] or mutually exclusive events or independent events so: Pr[K or Q] = Pr[K] + Pr[Q] = 4/52 + 4/52 = 8/52 = 2/13

A and B (Both events A and B occurring) - Intersection or  (shaped Area) also called Joint Probability
 

Venn Diagram - Union of A or B	Multiplication Rule for Independent Events: Prob (A and B) P(A and B) = P(A) x P(B) Joint Probability
Definition Intersection: Events A and B intersect if they both occurs at the same time. Example: The probability of getting both a Queen and a Heart. Number of Queens = 4, Sample space = 52 Number of Hearts = 13 Number of Queens and Hearts = 1	Rule Example: What is the probability of getting a Queen and a Heart from selecting a card from a deck of cards. P(Queen or Heart)=P(Queen)xP(Heart) P(Queen and Hearts) =

The complement of event A (not A) - Complement of A or  (S)
 

Venn Diagram - Complement of A	Probability of Complement: Prob (not A)
Definition: The complement of A is the event that event when it occurs event A does not occurs and when A occurs it does not occur. Example: The probability of not getting a Queen. Number of Queens = 4, Sample space = 52 Number of Non Queen cards = 48	Rule Example: What is the probability of not getting a Queen in selecting a card from a deck of cards. P(no Queen)=1 - P(Queen) P(no Queen) =

The probability of at least one - see example

"At least One" is the opposite of "None", so if event A is the probability of the event

We have Pr[A] = a  ( given)  and so  Pr[None] = 1 - Pr[A] = 1 - a

Or the Pr[at least one] = 1 - Pr[none]

Workshop Problem: Probability of Compound Events

From the number demographics study panelist problem:
 

Occupation	Family Income			Total
	Low	Medium	High
Homemaker	8	26	6	40
Blue-collar Worker	16	40	14	70
White-collar Worker	6	62	12	80
Professional	0	2	8	10
Total	30	130	40	200

If one person is selected at random from this group.

(a) Find the probability that the selected person is

(1) a homemaker or Blue-collar worker

(3) not homemaker worker (4) a professional and homemaker

(b) Find the probability that the selected person's family income is low and professional (two ways - hint use compliment)..

(c) Find the probability that the selected person is

(1) a white-collar worker and a high income

(2) a homemaker or a low income

(3) a professional and a medium income