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
What this standard means
Students need to define a random variable from a clear situation, list its possible values, and assign each value a probability using counting or probability rules. Then they calculate expected value by multiplying each value by its probability and adding the products.
Mastery looks like a complete probability table, probabilities that add to 1, and an expected value with the right meaning in context. Students often mix up outcomes and random variable values, skip combined cases, or treat expected value as the most likely outcome instead of a long-run average.
Ways to teach it
- Use a bag of colored cubes, define winnings by color, build the probability table, and compute expected winnings per draw.
- Ask students: Is a game fair if its expected value is zero, and who benefits if it is not?
- Give a three-question true-false guessing quiz and ask for the probability distribution for number correct, then check the expected value.
- Compare lottery scratch-off prize tables with ticket cost and have students calculate the expected gain or loss per ticket.
Plan a lesson for CCSS.Math.Content.HSS-MD.A.3
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Related standards
- CCSS.Math.Content.HSS-MD.B.5
(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
- CCSS.Math.Content.HSS-MD.A.4
(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value...
- CCSS.Math.Content.HSS-MD.A.1
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability dist...
- CCSS.Math.Content.HSS-MD.A.2
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.