Conditional Probability and Independence (Lesson 5.4)
Chapter 5  Day 4
Chapter 5
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
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Learning Targets

Find and interpret conditional probabilities using twoway tables.

Use the conditional probability formula to calculate probabilities.

Determine whether two events are independent.
Experience First
In this lesson, we continue using the Taco Tongue, Evil Eyebrow data that was collected in Lesson 5.3. Today we will determine if these two skills are independent of each other.
Students will work in small groups up to the STOP sign in the activity (#14). At this point, you should debrief the first part of the activity and also introduce the idea of a conditional probability, as well as the notation used for conditional probability. Students need to be familiar with the notation in order to be able to complete #5 in the activity.
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Formalize Later
When debriefing questions #2  3 in the activity, encourage students to first identify the given condition. Once they know the condition, they should go to the twoway table and circle the part of the table that is the given condition (this is most often one row or one column). Then students can find their conditional probability by using only the circled data. For example, the given condition in #3 is “No Evil Eyebrow”, so students should circle the column for No Evil Eyebrow. This column has 12 total students, 5 of which that are Yes Taco Tongue. Therefore P(Yes T.T.  No E.E.) = 5/12.
Work hard to help students have a thinking and reasoning understanding of independent and not a memorized formula. It is much better for students to know that “one event happening does not change the probability of the other event” rather than having memorized the formula to check for independence.