Florida B.E.S.T. MA.912.DP.6.5

MathGrades 9–12Use probability distributions to solve problems.

The Standard

Solve real-world problems involving geometric distributions.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students model repeated independent trials with the same probability of success and count trials until the first success. They calculate probabilities for when that success occurs and interpret the answer in context.
What Mastery Looks Like: Students identify the success event, the constant success probability, and the trial being counted. They choose the correct geometric formula, calculate accurately, and explain the result in context.
Common Misconceptions: Students may count failures instead of total trials, shifting the answer by one. They may also use a geometric model when trials are dependent or the success probability changes.
How to Assess It: Exit ticket: A player makes each free throw with probability 0.7. Find the probability that the first make occurs on shot four, then interpret your answer.

Lesson moves

Have pairs roll a die until a six appears, record the trial count, and compare class frequencies with geometric probabilities.
Ask students to explain why drawing cards without replacement usually does not fit a geometric distribution.
Give teams scenario cards to sort into geometric or not geometric, then calculate probabilities for the geometric cases.
Model product inspections by finding the probability that the first defective item appears on a given inspection.

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