Course detail

Probability

FP-pravPAcad. year: 2026/2027

Students will be able to apply classical and conditional probability in decision making in business processes.
Students will learn to apply methods of system reliability analysis and decision making under risk.
Students will be able to use random variables and special types of distributions to model and simulate business processes.
Students will learn to use decision trees and composite indices to optimize decision-making processes in businesses.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

Ing. Karel Doubravský, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

Not applicable.

Rules for evaluation and completion of the course

COMPLETION OF THE COURSE

Credit is awarded on the basis of:
- the completion of control tests;
- active participation in exercises.

The exam is written and consists of:
- solving four examples in 80 minutes;
- answering three theoretical questions in 15 minutes.

A mark, corresponding to a total (max. 100 points), consisting of:
- the score of the control tests (max. 40 points);
- the results of the examples solved (max. 48 points);
- the quality of the answers to the theoretical questions (max. 12 points).

Grades and their corresponding points:
A (100-90), B (89-80), C (79-70), D (69-60), E (59-50), F (49-0).

Attendance at lectures is not compulsory but is recommended. Attendance at tutorials is supervised. Any non-participation greater than 20 % will be made up with make-up assignments.

COMPLETION OF THE COURSE FOR STUDENTS WITH INDIVIDUAL STUDIES

Credit is awarded based on:
- completion of review assignments.

The exam is written and consists of:
- solving four examples in 80 minutes;
- answering three theoretical questions in 15 minutes.

A mark, corresponding to the total (max. 100 points), consisting of:
- the score of the control problems (max. 40 points);
- the results of the examples solved (max. 48 points);
- the quality of the answers to the theoretical questions (max. 12 points).

Grades and corresponding points:
A (100-90), B (89-80), C (79-70), D (69-60), E (59-50), F (49-0).

Aims

Students will be able to apply classical and conditional probability in decision making in business processes.
Students will learn to apply methods of system reliability analysis and decision making under risk.
Students will be able to use random variables and special types of distributions to model and simulate business processes.
Students will learn to use decision trees and composite indices to optimize decision-making processes in businesses.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

KROPÁČ, Jiří. Statistika A. 2.vydání. Brno: Akademické nakladatelství CERM, 2012. ISBN 978-80-7204-788-8. (CS)
MONTGOMERY, Douglas C. a RUNGER, George C. Applied statistics and probability for engineers: a study guide accompany. 7. vydání. New York: Wiley, 2018. ISBN 978-1-119-68890-7. (EN)
 ROSS, Sheldon M. Introduction to Probability and Statistics for Engineers and Scientists. 6. vydání. New York: Academic Press, 2020. ISBN 978-0-12-824346-6. (EN)
Studijní materiály dostupné na platformě Moodle. (CS)
ŘEZANKOVÁ, Hana; LÖSTER, Tomáš a ŠULC, Zdeněk. Úvod do statistiky. 2., přepracovaného vydání. Praha: Oeconomica, 2019. ISBN 978-80-245-2301-9. (CS)

Recommended reading

KROPÁČ, Jiří. STATISTIKA. 1. vydání. Brno: Akademické nakladatelství CERM, 2010. ISBN 978-80-214-3866-8.  (CS)
DANIELSON, Mats a EKENBERG, Love. Real-Life Decision-Making. 1. vydání. Boca Raton: CRC Press, 2023. ISBN 978-1-03-252438-2.   (EN)
KARPÍŠEK, Zdeněk. Matematika IV: statistika a pravděpodobnost. 4., přepracované vydání. Brno: Akademické nakladatelství CERM, 2014. ISBN 978-80-214-4858-2. (CS)
MAREK, Luboš. Pravděpodobnost. Praha: Professional Publishing, 2012. ISBN 978-80-7431-087-4. (CS)

Classification of course in study plans

  • Programme BAK-MIn Bachelor's 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Ing. Karel Doubravský, Ph.D.

Syllabus

Basic thematic content of the lectures:

1. Classical probability
2. Conditional probability
3. Random variable
4. Special discrete types of distribution of random variables
5. Special continuous types of distribution of random variables
6. Moivre-Laplace theorem
7. Reliability of systems
8. Random vector
9. Markov chains
10. Individual indices
11. Composite indices
12. Decision making under risk
13. Decision trees

Exercise

26 hours, compulsory

Teacher / Lecturer

Ing. Karel Doubravský, Ph.D.

Syllabus

Basic thematic content of the exercise:

1. Classical probability
2. Conditional probability
3. Random variable
4. Special discrete types of distribution of random variables
5. Special continuous types of distribution of random variables
6. Moivre-Laplace theorem
7. Reliability of systems
8. Random vector
9. Markov chains
10. Individual indices
11. Composite indices
12. Decision making under risk
13. Decision trees

 

Competencies

  • Students will understand classical and conditional probability and their application to business processes.
  • Students will be familiar with random variables and special types of distributions for modeling and simulating business processes.
  • Students will have an understanding of methods for system reliability analysis and decision making under risk.

Professional competences

  • Students will be able to apply classical and conditional probability to decision making in business processes.
  • Students will be able to use random variables and special types of distributions to model and simulate business processes.
  • Students will be able to apply methods of system reliability analysis and decision making under risk.

Professional skills

  • Students will learn to use decision trees and composite indices to optimize decision-making processes in enterprises.
  • Students will learn to model and simulate business processes using random variables and special types of distributions.
  • Students will learn to apply reliability analysis and risk-based decision-making methods in practical situations.

Self-study

34 hours, optionally

Teacher / Lecturer

Ing. Karel Doubravský, Ph.D.

Individual preparation for an ending of the course

70 hours, optionally

Teacher / Lecturer

Ing. Karel Doubravský, Ph.D.