The Multiplication Rule for Independent Events (Lesson 5.6)

Chapter 5 - Day 7

Learning Targets
  • Use the multiplication rule for independent events to calculate probabilities.

  • Calculate P(at least one) using the complement rule and the multiplication rule for independent events.

  • Determine if it is appropriate to use the multiplication rule for independent events in a given setting.

Activity: Can We Predict Snow Days and Traffic Jams? 
Activity:
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Experience First

First things first, we need to talk about what snow days. If you are live somewhere that has real winter, you already know (and so do your students). If you live somewhere in the south that never gets snow, let me fill you in. A snow day is a student’s greatest gift (also teachers): a day where the snow makes road travel dangerous, and school is cancelled. Snow days often occur together as a bad snowstorm might take several days to get the roads cleaned up. 

 

There is a STOP sign after question #4 in the activity so that you can introduce the big idea of this lesson: the probability of two independent events occurring is simply the product of the two probabilities.

 

Be ready to support students when they are working in their groups on questions #9 – 12. Here are some cues to have ready in your back pocket:

  • #9 “If there is a traffic jam every day of the week, doesn’t that mean there is a traffic jam on Monday AND a traffic jam on Tuesday AND a traffic jam on Wednesday AND….”

  • #10 “If there is no traffic jams all week, doesn’t that mean there is not a traffic jam on Monday AND not a traffic jam on Tuesday AND not a traffic jam on Wednesday AND….”

  • #11 “If it is NOT true that there was at least 1 traffic jam this week, what happened?”

  • #12 “What is the complement of at least 1 traffic jam (question #11). How do we find the probability of a complement of an event?”

Formalize Later

In Lesson 5.5 students learned the General Multiplication Rule:

 

P(A and B) = P(A)*P(B|A)

 

If A and B are independent, then knowing whether or not A occurs does not change the probability that B occurs. So P(B|A) = P(B) and the formula simplifies to the Multiplication Rule for Independent Events:

 

P(A and B) = P(A)*P(B)

 

This rule is simply a special case of the General Multiplication Rule.