Binomial Random Variables (Lesson 6.3 Day 1)
Chapter 6 - Day 4
Learning Targets
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Determine whether the conditions for a binomial setting are met.
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Calculate probabilities involving a single value of a binomial random variable.
Experience First
Notice first that we are using two days for Lesson 6.3. This first activity (Three Shots) really helps students to develop thinking and reasoning about the binomial formula. The second activity (Pop Quiz) will give them a chance to practice using the formula and technology.
The full basketball game is available on YouTube, but here are links that will take your right to the important parts of the game needed for this lesson. Be sure to review the lesson before teaching it so you are ready to pause the videos at the right time.
Students will work on questions #1-2 in the activity and then STOP. At this point, you should discuss the answers and then introduce the binomial formula. We suggest working through the remaining questions as a whole class.
Formalize Later
The best context for discussing the binomial formula is when calculating the probability of overtime.
So what does the 3 represent? It is the number of ways of making 2 and missing 1. This can also be calculated using a combination (3 choose 2). Discussing this idea with students is vital if they are to understand the binomial formula.
In the QuickNotes, you will present the four conditions for a binomial distribution (use the acronym BINS!) As you present each condition, be sure to note how it relates to the activity.
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Binary? “Success” = make free throw. “Failure” = miss free throw.
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Independent? Knowing whether or not one shot is made tells you nothing about whether or not the next shot is made.
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Number? n = 3.
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Same probability? p = 0.72.