The Multiplication Rule for Independent Events
Day 55 - Lesson 4.6
Use the multiplication rule for independent events to calculate probabilities.
Calculate P(at least 1) 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 traffic jams and snow days?
The big idea here is about independence. Knowing whether or not there is a traffic jam on Tuesday does not change the probability of a traffic jam on Wednesday. In other words, a traffic jam on Wednesday does not depend on whether there was a traffic jam on Tuesday. On the other hand, knowing whether or not there is a snow day on Tuesday does change the probability of a snow day on Wednesday. In other words a snow day on Wednesday does depend on whether there was a snow day on Tuesday. If there is a snow day on Tuesday, it is much more likely that there might be a snow day on Wednesday (maybe a big snow storm dumps a ton of snow).
Students struggled with question #8. We pointed them back to question #7 to help them recognize they needed to use the complement rule here.
Most students will try to calculate the probability for the final question as (0.7)(0.6) = 0.42. We pointed out that the 0.6 probability for Friday would probably go up if we knew that Thursday is a snow day, so we can’t calculate this probability.
In the Application and in the homework problems, students sometimes had trouble with P(none) in a given context. They wanted to find P(none) by taking the complement of P(all). These two events are not complements, as complementary events must comprise the whole sample space. What about P(1) or P(2) or P(3) etc?