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Unit 2 - Conditional Probability
Introduction to Statistics I (University of Calgary)
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Conditional Probability – 1
Unit 2: Conditional Probability
Textbook: 3.5, 3.6, (3.8)
Objectives:
Be familiar with the concept of conditional probability and be able to apply and
manipulate the conditional probability formula
Create and use a contingency table to find specific probabilities
Create and use a tree diagram to find specific probabilities
Prove independence/dependence using probability
Motivation
In Unit 1, we looked at some basic probability problems where no conditions were
assumed apart from those conditions that defined the experiment.
Examples (from Unit 1)
If I flip a fair coin 3 times in a row, what is the chance that I will get 3 heads?
How likely are the Dodgers to win the World Series this year?
What is the chance that I will miss my bus this evening?
While problems such as these might be interesting to us in many situations, there are
other situations where we may be interested in calculating the probability of something
occurring given some certain conditions.
Examples
If I flip a fair coin 3 times in a row and the first coin comes up heads, what is the
chance that I will get 3 heads in total?
Assuming that the Dodgers win the National League Championship Series (NLCS)
this year, how likely are they to win the World Series?
Given that I am delayed 3 minutes by a phone call this evening, what is the chance
that I will miss my bus?
These probabilities are a bit different from those presented in Unit 1 in the sense that
they rely in part on additional information or conditions (the first coin being a “heads,”
the Dodgers winning the NLCS, me being 3 minutes behind schedule).
These probabilities are what we call conditional probabilities. In this set of notes, we’ll
discuss the rules for calculating conditional probabilities as well as a few techniques that
can help make these calculations easier and more intuitive.
Downloaded by Kelvin Mulimi ()
Unit 2 - Conditional Probability
Introduction to Statistics I (University of Calgary)
Scan to open on Studocu
Studocu is not sponsored or endorsed by any college or university
Downloaded by Kelvin Mulimi ()
, lOMoARcPSD|56450245
Conditional Probability – 1
Unit 2: Conditional Probability
Textbook: 3.5, 3.6, (3.8)
Objectives:
Be familiar with the concept of conditional probability and be able to apply and
manipulate the conditional probability formula
Create and use a contingency table to find specific probabilities
Create and use a tree diagram to find specific probabilities
Prove independence/dependence using probability
Motivation
In Unit 1, we looked at some basic probability problems where no conditions were
assumed apart from those conditions that defined the experiment.
Examples (from Unit 1)
If I flip a fair coin 3 times in a row, what is the chance that I will get 3 heads?
How likely are the Dodgers to win the World Series this year?
What is the chance that I will miss my bus this evening?
While problems such as these might be interesting to us in many situations, there are
other situations where we may be interested in calculating the probability of something
occurring given some certain conditions.
Examples
If I flip a fair coin 3 times in a row and the first coin comes up heads, what is the
chance that I will get 3 heads in total?
Assuming that the Dodgers win the National League Championship Series (NLCS)
this year, how likely are they to win the World Series?
Given that I am delayed 3 minutes by a phone call this evening, what is the chance
that I will miss my bus?
These probabilities are a bit different from those presented in Unit 1 in the sense that
they rely in part on additional information or conditions (the first coin being a “heads,”
the Dodgers winning the NLCS, me being 3 minutes behind schedule).
These probabilities are what we call conditional probabilities. In this set of notes, we’ll
discuss the rules for calculating conditional probabilities as well as a few techniques that
can help make these calculations easier and more intuitive.
Downloaded by Kelvin Mulimi ()
