26134 Business Statistics Mahrita.Harahap@uts.edu.au

Tutorial 7: ProbabilityKey concepts in this tutorial are listed below

1. Construct contingency table 2. Understand Joint events

3. Understand joint probability 4. Understand marginal probability

5. Understand Conditional probability 6. Test of Independence

7. Practically apply the above concepts and calculate required probabilities

1

2

Quiz 2 in NEXT WEEK!!!!The topics to be tested in Quiz 2 are:THRESHOLD 3: Relating variables and analyzing relationships between variables.The specific topics for this threshold are: 1.) Lecture Topic: Simple Linear Regression 2.) Lecture Topic: Multiple Linear Regression 3.) Lecture Topic: Issues with Regression - Specific topics that will be tested in this lecture are : Use of Dummy Variables in regression and Multicollinearity.THRESHOLD 4: Theoretical foundation of statistical inference-Understanding events and using data to calculate the probability of occurrence of an event.The specific topics for this threshold are: 1.) Lecture Topic: ProbabilityThe sample quiz will be uploaded one week prior to the quiz.

Probability and Events

• Probability (P) is defined as the likelihood (or chance) that an event (A) will occur.

• Sample Space: is the set of all possible outcomes of an experiment.

• Event: an outcome of an experiment • An event is composed of one or more

elementary events.

3

4

Complement Events

• The events " rain in Sydney" and “no rain in Sydney” are complementary events. The complement of any event A is the event [not A], i.e. the event that A does not occur. Both these cannot occur at the same time. If A denotes the event of rain in Sydney then the probability of that event to not occur would be denoted as:

P(A’)=1− (A)𝑃5

6

Mutually-Exclusive Events• Occurrence of one event precludes the

occurrence of the other event. Event A and event B cannot occur at the same time.

P( ∩ )=0𝐴 𝐵• Events A and B are mutually exclusive if when A occurs, B

cannot occur and vice versa. Example of mutually exclusive events: A – Observing a 1 on the die roll, B – observing a 3 on the die roll.

7

8

Intersection and Union Events

• Intersection defined as probability of A and B occuring at the same time and is denoted as

P( ∩ )𝐴 𝐵• Union is defined as probability of A or B occurring at

the same time denoted a:

P(A U B) = P(A) + P(B) – P(A ∩ B)

9

10

11

A contingency table is also referred to as the frequency table. Similarly, probability table is also referred to as the relative frequency table.

12

P(D) = 0.58. This is an example of marginal probability. NOTE: Row totals or column totals are referred to as marginal probabilities.

NOTE: Mutual exclusive means cannot occur at the same time.

13

NOTE: the key to recognise questions on conditional probability is the word, given.

14

15