Lesson 8

Conditional Probability

Lesson Narrative

The mathematical purpose of this lesson is for students to make sense of conditional probability, the relationship between conditional probabilities and the probability that two events both occur, and to use conditional probability to investigate independence. Students encounter the term conditional probability in this lesson which is defined as the probability that one event occurs under the condition that another event occurs. The work of this lesson connects to previous work because students use probability to investigate dependence and independence. The work of this lesson connects to upcoming work because students will create and use two-way tables to estimate conditional probabilities. When students do the same type of calculation several times and observe that $$P(\text{A and B}) = P(\text{A | B}) \boldcdot P(\text{B})$$ for events A and B they are looking for and expressing regularity in repeated reasoning (MP8).

Learning Goals

Teacher Facing

• Comprehend (in written language) that the notation $P(\text{A and B}) = P(\text{A | B}) \boldcdot P(\text{B})$ can be used to find the conditional probability for events A and B.
• Use conditional probability to justify (orally and in writing) that events are dependent or independent.

Student Facing

• Let’s examine conditional probability.

Student Facing

• I can estimate probabilities, including conditional probabilities, from two-way tables.

Building Towards

Glossary Entries

• conditional probability

The probability that one event occurs under the condition that another event occurs.

• dependent events

Dependent events are two events from the same experiment for which the probability of one event depends on whether the other event happens.

• independent events

Independent events are two events from the same experiment for which the probability of one event is not affected by whether the other event occurs or not.

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