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Binomial Random Variables (Lesson 6.3 Day 2)

Chapter 6 - Day 5

Learning Targets
  • Determine whether the conditions for a binomial setting are met.

  • Calculate probabilities involving a single value of a binomial random variable.

  • Make a histogram to display a binomial distribution and describe its shape.

Activity: How Will Your Do on the Pop Quiz?

Experience First

Start this lesson by announcing there will be a pop quiz! And the hardest part about this quiz is that students don’t even get to see the questions. They have to guess on all 5 multiple choice questions. Read off the correct answers to the class and let them grade their own quizzes. Be sure to celebrate any students that might pass the quiz. 


This activity is a chance for students to practice the two learning targets from the previous lesson:

  • Checking conditions for a binomial distribution (BINS)

  • Using the binomial formula that came from the previous lesson. 


The new learning for this lesson is the third learning target: making a histogram for a binomial distribution. 

Formalize Later

By doing the Three Shots activity in the previous lesson, students should have a good conceptual understanding of the binomial theorem. Consider using the same language as you did during Three Shots: Success = Make and Failure = Miss.  When working through a binomial problem, we will often ask, “How many makes? What’s the probability? How many misses? What’s the probability?”  Students get really used to this pattern and find binomial probability fairly easy, which no one would expect when you look at the formula the first time!


We also suggest helping students to think about the binomial formula with words rather than symbols.


nCr = “the number of ways to get r successes in n trials”

p = “probability of success” 

r = “number of successes” 

(1 – p) = “probability of failure”

n – r =  “number of failures” 

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So instead of memorizing the binomial formula with variables, we say it is “the number of ways to get r successes in n trials, multiplied by the probability of success raised to the number of successes, multiplied by the number of failures raised to the number of failures”. 

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