Geometry Probability Checkpoint
A free Geometry lesson from the “Probability” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint reviews conditional probability, independence, area models, and geometric probability so the final course unit has the same assessment rhythm as the rest of Geometry. In Probability, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Review the major skills from this part of Geometry
- Connect diagram evidence to algebraic or written reasoning
- Check answers against units, figures, and proof logic
Worked example
Problem. Worked example from Conditional Probability and Independence: Roll a fair die. P(showing 4 | result is even) as a fraction.
- Given even = sample {2, 4, 6}, three outcomes.
- Of those, 4 is one. P = 1/3.
- Connect the result back to Geometry Probability Checkpoint so the geometric relationship is explicit.
- Check the result against the original diagram, units, or proof statement.
Answer: 1/3
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Geometry Probability Checkpoint review case A from Conditional Probability and Independence: Roll a fair die. P(showing 4 | result is even) as a fraction.
Show solution
- Given even = sample {2, 4, 6}, three outcomes.
- Of those, 4 is one. P = 1/3.
Answer: 1/3
2. Geometry Probability Checkpoint review case B from Conditional Probability and Independence: Roll a fair die. P(showing 6 | result is greater than 3) as a fraction.
Show solution
- Greater than 3 = {4, 5, 6}, three outcomes.
- Of those, 6 is one. P = 1/3.
Answer: 1/3
3. Geometry Probability Checkpoint review case C from Conditional Probability and Independence: If two events are independent, P(B | A) equals:
Choices: P(B) · P(A) * P(B) · P(A)
Show solution
- Independence means A does not change B's probability.
Answer: P(B)
4. Geometry Probability Checkpoint review case D from Conditional Probability and Independence: 100 students. 40 play sports; 30 are in band; 12 do both. Find P(band | sports) as a fraction.
Show solution
- P(band AND sports) / P(sports) = 12 / 40.
Answer: 12/40
5. Geometry Probability Checkpoint review case E from Conditional Probability and Independence: Same survey. Find P(sports | band) as a fraction.
Show solution
- P(sports AND band) / P(band) = 12 / 30.
Answer: 12/30
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