Unit 9 Probability

Lesson 1

Learning Focus

Create and use area models to determine theoretical probability of an outcome.

Lesson Summary

In today’s lesson, students used area models to determine the probabilities of compound events. Area models visually represent the probability of an outcome as a fraction of the total area of a geometric figure representing the sample space of all possible outcomes of an event. The probability of an outcome can be calculated using area formulas.

Lesson 2

Learning Focus

Interpret medical testing results using conditional probability.

Use a tree diagram to find probabilities.

Lesson Summary

In this lesson, we learned about conditional probability, the probability of an event given that another event has occurred. We used basic probability statements along with conditional probability to analyze the effectiveness of a medical test and to consider the meaning of testing errors, false positives, and false negatives.

Lesson 3

Learning Focus

Make Venn diagrams, tree diagrams, and two-way tables for data.

Use representations to find probabilities.

Lesson Summary

In this lesson, we learned to use two-way tables and Venn diagrams, along with tree diagrams, to find conditional, compound, and basic probabilities. We compared the representations to understand what information is easy to read from a given representation and what information may not be as evident in a representation, so that we can make choices about the representations we use for a given situation.

Lesson 4

Learning Focus

Use Venn diagrams to find probabilities.

Lesson Summary

In this lesson, we used Venn diagrams to find the probability of the complement of an event, the union of two events, and the intersection of two events. We learned that the probability of the union of two events can be found using the Addition Rule, $P (A or B) = P (A) + P (B) - P (A and B)$ .

Lesson 5

Learning Focus

Represent probabilities with Venn diagrams.

Use conditional probability to draw conclusions.

Understand the definition of conditional probability.

Lesson Summary

In this lesson, we learned the definition of conditional probability and the relationship with the union of two events. We discussed two events that cannot occur together and learned that they are called mutually exclusive. Finally, we were introduced to the idea of independent events, events that may occur together, but the probability of one event does not change if the other occurs.