ST102 : Introduction to the science of Probabilities

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

03

Prerequisite

ST101

Overview

This course introduces students to the principles and foundations of probability. It also deals with basic concepts of probability science, such as random experiments, sample space, the event and its types, and algebraic operations on it. This course also aims at developing the student’s ability to use sample space counting methods, methods of calculating probability, as well as distinguishing between conditional probability and independence,finally the course aims at enhancing students' skills in using Bayes' theorem.

Intended learning outcomes

By the end of the course, the student should be able to:

1. Recognize the concept of a random experiment and its accompanying sample space, identify multiple random experiments and its associated compound space, and express on the compound space using the tree method or Cartesian multiplication

2. Compare the concept of an event with the concept of a simple and compound event and a group of all events.

3. Distinguish the algebraic operations on events and the expressions that represent them and the Venn forms that represent them.

4. Explain the counting methods for calculating the sample space and the event space using the rule of addition, multiplication, permutations and combinations.

5. Explain the definition of probability, conditional probability, its calculation methods, and axioms of probability, laws related to probability calculation, conditional probability, and Bayes' theory.

6. Connect the concept of sets with the concept of sample space as well as the difference between them.

7. Link the concept of subsets and the operation set theory with events.

8. Connect the tree method, the Cartesian multiplication method, and the counting methods in calculating the compound space.

9. connect the concept of relative frequency and the concept of probability in calculating them, using the experimental and classical methods

10. Deduce the postulates of conditional probability, the laws of conditional probability, the theory of total probability, and Bayes' theorem

11. Distinguish between the concept of independent events and mutually exclusive events.

12. Calculates the probability of the elements of a sample space using the classical method and the experimental method

13. Design random experiments and create an appropriate composite sample space using counting methods.

14. Practically, apply the theory of total probability and Bayes' theory

15. Calculate the probabilities in different ways for different spaces under the imposed conditions

16. Apply the postulates of conditional probability, the laws of conditional probability, the theory of total probability, and Bayes' theorem.

Teaching and learning methods

1. Practical and theoretical lectures

2. Discussion and dialogue

3. Brainstorm

4. Working papers, case study

5. Presentations

6. Videos and e-learning

7. Using software and computer applications such as (MATLAB, Geogebra, Geometer)

Methods of assessments

Methods of evaluating students in this course are:

1. A written exam (essay + objective) = 30 marks, or its assessment is left to the course instructor.

2. Short exams (written or oral), demonstration assignments and presentation applications = 10 marks or the assessment is left to the course instructor.

3. Written final exam (essay + objective) = 60 marks

Main content of the Course

Week	Scientific subject	Number of hours	Lecture	Exercises
1-2	Sample Space, Events, Algebraic Operations on Events, Venn Forms.	8	Ö	Ö
3-4	Counting methods: addition rule - multiplication rule - factorial	8	Ö	Ö
5	First midterm exam (2 hours)
5-6	Permutations and combinations	6	Ö	Ö
7-8	Probability: its concept, methods of calculation, axioms of probability – its laws.	8	Ö	Ö
9-10	Conditional probability: its concept, methods of calculation, axioms of – its laws.	6	Ö	Ö
10	Second midterm exam (2 hours)
11	Independent events: the concept of independence for two events - bilateral independence - triple independence - total independence.	4	Ö	Ö
12-13	Total probability theorem	8	Ö	Ö
14	Bayes' theorem	4	Ö	Ö
15-16	Final exam
	Total	56

References:

Title of references	Publisher	Version	Author	Located
Statistics and probabilities theory and practice""	Dar Al-Hikma	Second Edition	Dr. Ali Abd al Salam al Ammari Dr. Ali Hussein Al-Ajili	Public Libraries

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