CCSS.Math.Content.HSS-MD.A.3
The Standard
(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students define a discrete random variable from a sample space and list its possible values. They calculate each value’s theoretical probability and use the distribution to find the expected value.
What Mastery Looks Like
- Students can organize possible values and their theoretical probabilities in a correct table. They verify that the probabilities total 1 and calculate the expected value using each value times its probability.
Common Misconceptions
- Students may treat random-variable values as equally likely, even when different numbers of outcomes produce them. They may forget that all probabilities must total 1. They may also assume the expected value must be a possible single result.
How to Assess It
- Give this exit ticket: “A fair coin is flipped three times. Make the probability distribution for the number of heads, then find its expected value.”
Lesson moves
Ways to Teach It
Give pairs three coins and an outcome grid; they list all outcomes, group by heads, and build the probability table.
Ask, “Can an expected value be impossible as a single outcome?” Students answer using a two-spin prize example.
Play Distribution Match with cards showing sample spaces, random-variable values, probabilities, and expected values; teams assemble correct sets.
Analyze a carnival game with listed prizes and equally likely spinner sections, then calculate expected payout and choose a fair ticket price.
Free download
Printable HSS-MD.A.3 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSS-MD.A.3, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSS-MD.A.1
Finding expected value requires assigning numerical outcomes and organizing their probabilities as a distribution first.
- CCSS.Math.Content.HSS-MD.A.2
Finding expected value from a theoretical probability distribution requires calculating and interpreting the distribution’s mean.
- CCSS.Math.Content.HSS-CP.A.1
Probability distributions require grouping sample-space outcomes into events for each random variable value and calculating their theoretical probabilities.
What This Unlocks
Mastery here sets students up for these next.
Keep exploring
Related Standards
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.