Review of Basic Probability - Part 2
Objective:
By the end of this lesson, students will have reviewed the following topics:
- Independent/dependent events
- Multiplication Rule for independent events
- Conditional probability
- General Multiplication Rule for dependent events
Duration:
- 75 minutes
Materials:
- Handouts with exercises and problems related to basic probability
- Computer, projector, and screen
Introduction:
Examples that can be used to jump start topic:
Introduce the lesson’s topic:
- Today we will continue reviewing basic probability rules.
Historical Context:
1560s: Cardano wrote Liber de ludo aleae, the first known systematic treatment of probability, and as the result of a gambling addiction.
1654: Fermat and Pascal worked on the foundation of probability theory through correspondence.
1812 and 1814: Laplace published Théorie analytique des probabilités and Essai philosophique sur les probabilités, outlining many basic and fundamental results in statistics.
Main Content:
- Conditional probability: if \(A\) and \(B\) are any two events,
\[P(A|B) = \frac{P(A \cap B)}{P(A)}\]
- General Multiplication Rule for dependent events: the probability that two events \(A\) and \(B\) both occur is
\[P(A \cap B) = P(A) \times P(A|B)\]
- Independent/dependent events: two events, \(A\) and \(B\) are independent if
\[P(A|B) = P(A) \text{ or } P(B|A) = P(B)\]
- Multiplication Rule for independent events: when two events are independent,
\[P(A \cap B) = P(A) \times P(B)\]
Discussion and Wrap-Up:
- Facilitate a class discussion to review the example problems, reinforce key concepts, and answer any questions the students have.
Homework:
- Assign additional problems to practice the basic probability rules.
Formative Assessment:
- Evaluate students based on their participation in discussions, their ability to solve example problems, and their performance on the assigned homework.
Conclusion:
- Emphasize these are building blocks for the next lesson and long term understanding probability.