Introduction to Probability

Learning Objectives

• Define sample space and experiment

• Define probabilities

• Define random variable and distribution function

Set Theory

Sample Space

Event

\(S=\{a_1,a_2,a_3,a_4, a_5\}\)

Set Rules

\(S=\{a_1,a_2,a_3,a_4, a_5\}\)

Set Rules

\(S=\{a_1,a_2,a_3,a_4, a_5\}\)

Probability Functions

Enumerating outcomes

\(S=\{a_1,a_2,a_3,a_4, a_5\}\)

Probability Rules

Probability Rules

Random Variable

Random Variable

Probability Mass Function

Cumulative Density Function

Example

Example

Suppose we want to understand the efficacy of a test for a certain disease. Consider the following table:

		Disease	Presence	Total
		Yes	No
Test Result	Yes	42	6
	No	17	35
				100

Example

• Find the probability that an individual has a disease

• Find the probability that an individual tests negative for a disease

• Find the probability that and tests positive for a disease or they don’t have the disease

• Find the probability that the test gives an accurate result

• Find the probability that the test gives and inaccurate result