1. SECTION 4.3
ADDITION RULE 1

2. ADDITION RULE
Finding the probability of either event occurring.

3. VENN DIAGRAM
A pictorial graph of events. U U

4. ADDITION RULE
There are two situations
Overlap
Disjoint

5. OVERLAP There exists values that both events have in common.
Looking at a graph, there exist an area that both events connect with.
Because they overlap we are including those values/section twice, thus we must subtract one.

6. VENN DIAGRAM - OVERLAP

7. VENN DIAGRAM - OVERLAP

8. ADDITION RULE - OVERLAP
P(A È B) = P(A) + P(B) - P(A ∩ B) A and B : two events ∩ : and È : or

9. OVERLAP EXAMPLE
Given the table that summarizes the results of people who refused to answer the questions.
60 - over
Responded 73
255
245
136
138
202
Refused 11 20 33 16 27 49

10. OVERLAP EXAMPLE
What is the probability that the selected person responded or is in the 18 – 21 age bracket?

11. OVERLAP EXAMPLE
What is the probability that the selected person refused to respond or is over 59 years of age?

12. DISJOINT
The two events have nothing in common 12

13. VENN DIAGRAM - DISJOINT

14. VENN DIAGRAM - DISJOINT

15. ADDITION RULE FOR DISJOINT
Recall the Addition Rule
P(A È B) = P(A) + P(B) - P(A ∩ B)
For a disjoint situation P(A ∩ B) = 0
Therefore we can simplify the Addition Rule
P(A È B) = P(A) + P(B) 15

16. DISJOINT EXAMPLE
Jennifer and Bill draw a card from the deck of What is the probability that they get either an Ace or a King?

17. DISJOINT EXAMPLE
A pair of dice is thrown. What would the probability be of rolling a 6 or an 11?