Illustrative Mathematics
Fred's Fun Factory
Spin to win! Individuals calculate the average number of tickets expected based on a probability distribution for the number of tickets per spin. Pupils use that information to determine the average number of tickets that can be won...
EngageNY
End-of-Module Assessment Task - Precalculus (Module 5)
Give your young scholars a chance to show what they've learned from the module. The last installment of a 21-part series is an end-of-module assessment task. It covers basic and conditional probabilities, expected value, and...
College Board
2010 AP® Statistics Free-Response Questions Form B
Form a good familiarity with the AP® test using Form B of the 2010 AP® Statistics free-response questions. Pupils use a test from a previous administration to prepare for their exams. A set of six questions assesses box plots,...
College Board
2003 AP® Statistics Free-Response Questions Form B
Update the statistics in your course using older AP® questions. The 2003 AP® Statistics free-response questions cover several of the concepts in the current statistics standards for all pupils. Items contain questions about...
College Board
1999 AP® Statistics Free-Response Questions
Closer to 2010 than expected. Several of the 1999 AP® Statistics free-response questions align to Common Core standards. Items ask pupils to analyze residuals, two-way tables, and calculate expected values to determine the fairness...
College Board
2015 AP® Statistics Free-Response Questions
Statistics is all about making inferences. Can you infer how your pupils will fair on their AP® exams? Collect your own data by giving them practice tests such as the 2015 free-response exam. The six-question test includes topics such as...
Illustrative Mathematics
Rolling Dice
Rolling dice is a great way for your mathematicians to get a hands-on approach to probabilities. Use the chart to record whether they rolled a six during ten attempts. Calculate results individually (or in small groups) and then record...
Curated OER
Fred's Fun Factory
Round and round and round she goes. Where she stops, nobody knows. This activity uses a common arcade game of chance, the spinning wheel, as a platform for computing expected values, interpreting results, and applying this knowledge to...
Illustrative Mathematics
Sounds Really Good! (Sort Of...)
Winning a lottery game with 60% odds sounds like a no brainer. This is when the math kicks in to show players that in the long run, they lose money the more often they play. Here is one simple question that opens the doors to a nice...
Curated OER
Bob's Bagel Shop
How much money can Bob expect to make per customer by selling bagels? This short expected value problem can be used as a warm up or a quick assessment at the end of a more detailed lesson. Teacher commentary includes the solution to the...
Curated OER
Sounds Really Good! (sort of...)
Your friend Phil wants to know if he should play the lottery. Have your class use the given data to compute the expected value and explain to Phil what he should do and why. This handout is ideal for a quick assessment of skill and...
College Board
2004 AP® Statistics Free-Response Questions
Provide some practice showing the work. Pupils work through six free-response questions that require them to show their work. They use their knowledge of statistics to develop solutions to problems within context. Scenarios range from...
College Board
2001 AP® Statistics Free-Response Questions
Develop a complete understanding of the course. Pupils and teachers use the six free-response questions to gather information about aspects of the AP® Statistics course. The resource and test section show how items cover the content. A...
EngageNY
Summarizing a Data Distribution by Describing Center, Variability, and Shape
Put those numbers to work by completing a statistical study! Pupils finish the last two steps in a statistical study by summarizing data with displays and numerical summaries. Individuals use the summaries to answer the statistical...
Khan Academy
Khan Academy: Expected Value With Calculated Probabilities
Find expected value based on calculated probabilities. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Expected Value With Empirical Probabilities
Find expected value based on empirical probabilities. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Making Decisions With Expected Values
Calculate expected values and then use them to make decisions. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Discrete Random Variables: Expected Value
Compute the expected value given a set of outcomes, probabilities, and payoffs. Students receive immediate feedback and have the opportunity to try questions repeatedly or receive hints.
Khan Academy
Khan Academy: Mean (Expected Value) of a Discrete Random Variable Practice
A practice word problem asking learners to calculate the mean of B in a probability chart.