Probability and Statistics

1. Math 210:
Probability and Statistics

2. Trisha Mae M. Ramos
 Graduated with a degree course of Bachelor of Secondary
Education major in Mathematics in the year 2015 as Cum
Laude at Tarlac Agricultural University
 Graduated Master of Arts in Mathematics Education with
specialization in Secondary School Teaching at Philippine
Normal University
 International Research Presenter
 DEPED Regional Outstanding Teacher- Region III
 DEPED Regional Content Writer and Validator
 Work at College of the Holy Spirit – Tarlac (2 Years)
 Department of Education- Tarlac Province (4 years)
 Chair of Curriculum and Instruction, TAU-CEd

4. List of Topics for the Course
 Basic Counting Principle
 Permutation
 Combination
 Mathematical Probability
 Sample Spaces
 Events (Subsets, Mutually
Exclusive)
 Axioms of Probability
 Finite Probability Space
 Finite Equiprobable Space
 Conditional Probability
 Tree Diagramming
 Random Variables
 Binomial, Hypergeometric and
Poisson Distribution
 Joint Probability Mass Functions

5. Basic Counting Rule (Fundamental)
• Suppose that r actions are to be represented in a definite order.

6. Examples of Basic Counting Rule
• Five people are to sit in a car, 2 in front and 3 at the back. How many arrangement can be made if 2 do not
know how to drive?

7. Examples of Basic Counting Rule
• Given 1, 3, 5 , 7, 8, 9
• How many 3 digit number can be formed?
• How many are even?
• How many are odd?
• How many are multiples of 5?

8. Permutation
• An arrangement of a set of M objects in a given action of the objects

9. Permutation
• An arrangement of a set of M objects in a given action of the objects

10. Linear Permutation
• Number of permutations of M taken r at a time.

11. Permutation with Repetition
• The number of permutation of m object of which m, are alike m2 are alike, …. is

12. Circular Permutation
• In genera, number digit can be arranged in a circle m ways.

13. Examples of Permutation
• In how many was can 3 boys and 2 girls sit in a row?

14. Examples of Permutation
• In how many ways can 3 boys and 2 girls sit if the boys and girls are each to sit together.

15. Examples of Permutation
• In how many ways can 3 boys and 2 girls if just the girls are to sit together?

16. Examples of Permutation
• In how many ways can 3 boys and 3 girls sit around a circular table?

17. How many ways can a chairperson and an assistant chairperson be
selected for a research project if there are seven persons available?

18. Examples of Permutation
• How many permutations are there in the word: CALCULUS.

19. Examples of Permutation
• Find x if:
• P(x,2) = 72

20. Examples of Permutation
• Find x if:
• P(x,4) = 42 P(x,2)

21. Combination
• A combination of r objects for a collection of M objects is any…

22. Examples of Combination
• A delegation of 4 students is selected to attend a meeting:
• In how man ways can the delegation be chosen if there are 12 eligible students?

23. Examples of Combination
• A delegation of 4 students is selected to attend a meeting:
• In how man ways can the delegation be chosen if there are 12 eligible students but two students will
not attend the meeting together?

24. Examples of Combination
• A delegation of 4 students is selected to attend a meeting:
• In how man ways can the delegation be chosen if there are 12 eligible students but two students will
only attend the meeting together?