C.M. Pascual

26
1 C.M. Pascual C.M. Pascual STATISTICS Chapter 5b Probability Addition Rule

description

S TATISTICS. Chapter 5b Probability Addition Rule. C.M. Pascual. Compound Event Any event combining 2 or more simple    events. Definition. Compound Event Any event combining 2 or more simple    events Notation - PowerPoint PPT Presentation

Transcript of C.M. Pascual

Page 1: C.M. Pascual

1C.M. Pascual

C.M. PascualC.M. Pascual

STATISTICS

Chapter 5b Probability Addition Rule

Page 2: C.M. Pascual

2C.M. Pascual

Compound Event Any event combining 2 or more simple    events

Definition

Page 3: C.M. Pascual

3C.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

Page 4: C.M. Pascual

4C.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

Page 5: C.M. Pascual

5C.M. Pascual

Formal Addition RuleP(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

Page 6: C.M. Pascual

6C.M. Pascual

Formal Addition RuleP(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 RuleTo 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

Page 7: C.M. Pascual

7C.M. Pascual

DefinitionEvents A and B are mutually exclusive if they

cannot occur simultaneously.

Page 8: C.M. Pascual

8C.M. Pascual

DefinitionEvents 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

Page 9: C.M. Pascual

9C.M. Pascual

DefinitionEvents A and B are mutually exclusive if they

cannot occur simultaneously.

Figures 3-5 and 3-6

Total Area = 1 Total Area = 1

P(A) P(B) P(A) P(B)

P(A and B)

Non-overlapping EventsOverlapping Events

Page 10: C.M. Pascual

10C.M. Pascual

Figure 5-7 Applying the Addition Rule

P(A or B)

Addition Rule

AreA and Bmutuallyexclusive

?

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

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

No

Page 11: C.M. Pascual

11C.M. Pascual

Find the probability of randomly selecting a man or a boy.

Men Women Boys Girls Totals

Survived 332 318 29 27 706

Died 1360 104 35 18 1517

Total 1692 422 64 56 2223

Contingency Table

Page 12: C.M. Pascual

12C.M. Pascual

Find the probability of randomly selecting a man or a boy.

Men Women Boys Girls Totals

Survived 332 318 29 27 706

Died 1360 104 35 18 1517

Total 1692 422 64 56 2223

Contingency Table

Page 13: C.M. Pascual

13C.M. Pascual

Find the probability of randomly selecting a man or a boy.

P(man or boy) = 1692 + 64 = 1756 = 0.7902223 2223 2223

Men Women Boys Girls Totals

Survived 332 318 29 27 706

Died 1360 104 35 18 1517

Total 1692 422 64 56 2223

Contingency Table

Page 14: C.M. Pascual

14C.M. Pascual

Find the probability of randomly selecting a man or a boy.

P(man or boy) = 1692 + 64 = 1756 = 0.7902223 2223 2223

Men Women Boys Girls Totals

Survived 332 318 29 27 706

Died 1360 104 35 18 1517

Total 1692 422 64 56 2223

Contingency Table

* Mutually Exclusive *

Page 15: C.M. Pascual

15C.M. Pascual

Find the probability of randomly selecting a man or someone who survived.

Men Women Boys Girls Totals

Survived 332 318 29 27 706

Died 1360 104 35 18 1517

Total 1692 422 64 56 2223

Contingency Table

Page 16: C.M. Pascual

16C.M. Pascual

Find the probability of randomly selecting a man or someone who survived.

Men Women Boys Girls Totals

Survived 332 318 29 27 706

Died 1360 104 35 18 1517

Total 1692 422 64 56 2223

Contingency Table

Page 17: C.M. Pascual

17C.M. Pascual

Find the probability of randomly selecting a man or someone who survived.

P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223

Men Women Boys Girls Totals

Survived 332 318 29 27 706

Died 1360 104 35 18 1517

Total 1692 422 64 56 2223

Contingency Table

= 0.929

Page 18: C.M. Pascual

18C.M. Pascual

Find the probability of randomly selecting a man or someone who survived.

P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223

Men Women Boys Girls Totals

Survived 332 318 29 27 706

Died 1360 104 35 18 1517

Total 1692 422 64 56 2223

Contingency Table

* NOT Mutually Exclusive *

= 0.929

Page 19: C.M. Pascual

19C.M. Pascual

Complementary Events

Page 20: C.M. Pascual

20C.M. Pascual

Complementary Events

P(A) and P(A)are

mutually exclusive

Page 21: C.M. Pascual

21C.M. Pascual

Complementary Events

P(A) and P(A)are

mutually exclusive

All simple events are either in A or A.

Page 22: C.M. Pascual

22C.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

Page 23: C.M. Pascual

23C.M. Pascual

Rules of Complementary Events

P(A) + P(A) = 1

Page 24: C.M. Pascual

24C.M. Pascual

P(A)

Rules of Complementary Events

P(A) + P(A) = 1

= 1 - P(A)

Page 25: C.M. Pascual

25C.M. Pascual

P(A) + P(A) = 1

= 1 - P(A)

P(A) = 1 - P(A)

P(A)

Rules of Complementary Events

Page 26: C.M. Pascual

26C.M. Pascual

Figure 5-8 Venn Diagram for the Complement of Event A

Total Area = 1

P (A)

P (A) = 1 - P (A)