Lesson Plan

The Improbability of You Winning the Lottery

Identifying the very, very slim chance of hitting the jackpot
Joseph E.
Classroom teacher
Huntington High School
Huntington, WV
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My Grades 10, 11
My Subjects Math

Students will be able to understand the probability of winning the lottery by using illustrative comparisons of finding probability of other things.

West Virginia CSOs:

M.2HS.AOP.2  -- understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities and use this characterization to determine if they are independent. 

M.2HS.AOP.9 -- use permutations and combinations to compute probabilities of compound events and solve problems.

M.2HS.AOP.10 --  use probabilities to make fair decisions

Grades 9 - 12
All Notes
Teacher Notes
Student Notes

1 Hook

Students will look up articles or watch news footage of people recently winning big lottery jackpots.  This will create a springboard toward dialogue what entices people to play and who in their lives has won the lottery. Ultimately, the teacher may need to steer the conversation toward the probability of winning the lottery.

2 Direct Instruction

IXL - Math and English
Free, Free to Try

Students will need to learn the concepts of permutations and combinations to better understand the probability of winning a prize in a lottery. Use this time to point out the key difference between a permutation versus a combination and why the term "combination lock" is a misnomer. IXL will reinforce the the basic skills of computing combinations and permutations.

3 Guided Practice

Students will research the rules of playing high-jackpot lottery games such as Powerball or Mega Millions.  They will need to discover that the game uses combinations instead of permutations.  (The balls drawn need not be in the exact order).

4 Independent Practice

Activity: Exploring

Students will simulate playing the lottery by either picking their own numbers or using a random number generator such as http://www.random.org.  The teacher will draw the "winning numbers", and students will check to see if they would have won any money.  The first time, students will only do one set, then five, then twenty, then 100.  The main idea is to determine whether or not multiple plays significantly affect the probability of winning. 

5 Wrap-Up

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Students will create a presentation and argumentative essay on whether they think taking out a second mortgage to buy lottery tickets for a one-billion dollar jackpot is a good idea or bad idea.  They will need to use the application of probabilities to explain the pros and cons of doing such a thing.