1. General Addition Rule
AP Statistics

2. Addition Rule for Disjoint Events
If two events A and B are disjoint:
P(A or B) = P(A) + P(B)
If three events are disjoint:
P(A or B or C) = P(A) + P(B) + P(C)

3. Mutually Exclusive (Disjoint) Events
Two events have no outcomes in common.
Example: An animal can’t be a dog and a cat at the same time.
Example: Roll a “2” or a “5” – these can’t happen at the same time.
Note: the second “or” statement involves only one roll of the die, not two rolls.

4. Venn Diagram - Disjoint EventsB
P(A or B) = P (A) + P(B)
Can also be written P(A B).
This is the union of events A and B.

5. Non –Disjoint Events: Can Have Outcomes in Common.
If two events E & F are not disjoint,
P(E or F) = P(E) + P(F) – P(E and F)
This is The General Addition Rule.
P(E and F) is called a joint probability and can be written P(E∩F).
P(E∩F) is also called the intersection of events E and F.

6. Non Disjoint Events A B
The shaded region shows the intersection of events A and B, where A and B can happen at the same time.

7. Example Event A = (Being a senior at CRHS)
Event B = (Taking Statistics)
You can have seniors at CRHS who are taking Stats! These events can happen at the same time.

8. Example 6.17 on page 362 P (Deb becoming a partner) = .7
P (Matt becoming a partner) = .5
P (Deb and Matt becoming a partner) = .3
P(Deb or Matt becoming a partner) = 1.2??
This probability exceeds 1 which is impossible!

9. Venn Diagram Interpretation
D and M
D and MC
DC and M
DC and MC
Let’s add in all the values for these 4 joint probabilities!

10. Example 6.17 Continued P(at least one is promoted) = P(Deb or Matt)
= = .9
P(neither is promoted) = 1-.9 = .1
The reason that we “correct” by subtracting .3 (the intersection of Deb and Matt) is that if we don’t, it is counted twice.

11. Union
The union of event A with event B consists of all outcomes that are in at least one of the two events.
Example: Event E is rolling a die and getting prime number or even number.
E = {2,3,4,5,6}

12. Venn Diagram - A or B A B
Event A consists of {2,3,5}. Event B consists of
{2,4,6}. A U B consists of {2,3,4,5,6}

13. Intersection This is the event where both A and B happen.
It consists of all outcomes that are in both events.
Denoted:

14. Venn Diagram - A and B A B
From the previous example, A∩B is {2}, which is both
an even and prime number.

15. General Rule for the Union of Two Events
P(A or B) = P(A) + P(B) – P(A and B).
Note: if there is no intersection (if A and B are mutually exclusive), then the term:
P(A and B) is equal to zero, which returns us to the Addition Rule for Disjoint Events.

16. Homework
Worksheet