Florida B.E.S.T. MA.912.DP.6.2
The Standard
Develop a probability distribution for a discrete random variable using theoretical probabilities. Find the expected value and interpret it as the mean of the discrete distribution.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students list every possible value of a discrete random variable and assign each value its theoretical probability. They calculate the weighted mean and explain what it predicts over many trials.
What Mastery Looks Like
- Students create a complete distribution with probabilities between 0 and 1 that sum to 1. They calculate the expected value and explain it as a long-run average in context.
Common Misconceptions
- Students may assume outcomes are equally likely or leave out possible values. They may average the values without weighting them, or think the expected value must be a possible single outcome.
How to Assess It
- Give this exit ticket: “A bag has 2 red and 3 blue counters. Red wins $4 and blue loses $1. Make the distribution, find the expected value, and interpret it.”
Lesson moves
Ways to Teach It
Give pairs two coins and an outcome tree to build the probability distribution for the number of heads.
Ask students to write whether a game with an expected payout of $0.50 is fair, then defend their answer.
Play a matching game where students pair probability tables with expected values and correct long-run interpretations.
Have students calculate a store’s expected profit on a warranty using possible repair costs and their theoretical probabilities.
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Related Standards
- MA.912.DP.6.3
Develop a probability distribution for a discrete random variable using empirical probabilities. Find the expected value and interpret it as the mean of the dis...
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Use probability distributions to solve problems.
- MA.912.DP.6.4
Given a binomial distribution, calculate and interpret the expected value. Solve real-world problems involving binomial distributions.
- MA.7.DP.2
Develop an understanding of probability. Find and compare experimental and theoretical probabilities.
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