1 C.M. Pascual S TATISTICS Chapter 5b Probability Addition Rule

2 C.M. Pascual  Compound Event Any event combining 2 or more simple events Definition

3 C.M. Pascual  Compound Event Any event combining 2 or more simple events  Notation P(A or B) = P (event A occurs or event B occurs or they both occur) Definition

4 C.M. Pascual General Rule When finding the probability that event A occurs or event B occurs, find the total number of ways A can occur and the number of ways B can occur, but find the total in such a way that no outcome is counted more than once. Compound Event

5 C.M. Pascual Formal Addition Rule P(A or B) = P(A) + P(B) - P(A and B) where P(A and B) denotes the probability that A and B both occur at the same time. Compound Event

6 C.M. Pascual Formal Addition Rule P(A or B) = P(A) + P(B) - P(A and B) where P(A and B) denotes the probability that A and B both occur at the same time. Intuitive Addition Rule To find P(A or B), find the sum of the number of ways event A can occur and the number of ways event B can occur, adding in such a way that every outcome is counted only once. P(A or B) is equal to that sum, divided by the total number of outcomes. Compound Event

7 C.M. Pascual Definition Events A and B are mutually exclusive if they cannot occur simultaneously.

8 C.M. Pascual Definition Events A and B are mutually exclusive if they cannot occur simultaneously. Figures 3-5 Total Area = 1 P(A) P(B) P(A and B) Overlapping Events

9 C.M. Pascual Definition Events A and B are mutually exclusive if they cannot occur simultaneously. Figures 3-5 and 3-6 Total Area = 1 P(A) P(B) P(A and B) Non-overlapping Events Overlapping Events

10 C.M. Pascual Figure 5-7 Applying the Addition Rule P(A or B) Addition Rule Are A and B mutually exclusive ? P(A or B) = P(A)+ P(B) - P(A and B) P(A or B) = P(A) + P(B) Yes No

11 C.M. Pascual Find the probability of randomly selecting a man or a boy. Men Women Boys Girls Totals Survived Died Total Contingency Table

12 C.M. Pascual Find the probability of randomly selecting a man or a boy. Men Women Boys Girls Totals Survived Died Total Contingency Table

13 C.M. Pascual Find the probability of randomly selecting a man or a boy. P(man or boy) = = 1756 = Men Women Boys Girls Totals Survived Died Total Contingency Table

14 C.M. Pascual Find the probability of randomly selecting a man or a boy. P(man or boy) = = 1756 = Men Women Boys Girls Totals Survived Died Total Contingency Table * Mutually Exclusive *

15 C.M. Pascual Find the probability of randomly selecting a man or someone who survived. Men Women Boys Girls Totals Survived Died Total Contingency Table

16 C.M. Pascual Find the probability of randomly selecting a man or someone who survived. Men Women Boys Girls Totals Survived Died Total Contingency Table

17 C.M. Pascual Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = = Men Women Boys Girls Totals Survived Died Total Contingency Table = 0.929

18 C.M. Pascual Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = = Men Women Boys Girls Totals Survived Died Total Contingency Table * NOT Mutually Exclusive * = 0.929

19 C.M. Pascual Complementary Events

20 C.M. Pascual Complementary Events P(A) and P(A) are mutually exclusive

21 C.M. Pascual Complementary Events P(A) and P(A) are mutually exclusive All simple events are either in A or A.

22 C.M. Pascual Complementary Events P(A) and P(A) are mutually exclusive All simple events are either in A or A. P(A) + P(A) = 1

23 C.M. Pascual Rules of Complementary Events P(A) + P(A) = 1

24 C.M. Pascual P(A) Rules of Complementary Events P(A) + P(A) = 1 = 1 - P(A)

25 C.M. Pascual P(A) + P(A) = 1 = 1 - P(A) P(A) = 1 - P(A) P(A) Rules of Complementary Events

26 C.M. Pascual Figure 5-8 Venn Diagram for the Complement of Event A Total Area = 1 P (A) P (A) = 1 - P (A)