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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

Why it matters: Geometry assessments mix diagram reading, formulas, coordinates, proof logic, and context so students practice choosing evidence rather than memorizing a single cue.

Worked example

Problem. Worked example from Conditional Probability and Independence: Roll a fair die. P(showing 4 | result is even) as a fraction.

  1. Warm-up: First identify exactly what the question is asking: Roll a fair die. P(showing 4 | result is even) as a fraction.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Given even = sample {2, 4, 6}, three outcomes.
  4. Of those, 4 is one. P = 1/3.

Answer: 1/3

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
  1. Warm-up: First identify exactly what the question is asking: Roll a fair die. P(showing 4 | result is even) as a fraction.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Given even = sample {2, 4, 6}, three outcomes.
  4. Of those, 4 is one. P = 1/3.
  5. Check the result by substituting or estimating: the response should match 1/3 and make sense in the original problem.

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
  1. Warm-up: First identify exactly what the question is asking: Roll a fair die. P(showing 6 | result is greater than 3) as a fraction.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Greater than 3 = {4, 5, 6}, three outcomes.
  4. Of those, 6 is one. P = 1/3.
  5. Check the result by substituting or estimating: the response should match 1/3 and make sense in the original problem.

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
  1. Warm-up: First identify exactly what the question is asking: If two events are independent, P(B | A) equals:
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Independence means A does not change B's probability.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

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
  1. Core Practice: First identify exactly what the question is asking: 100 students. 40 play sports; 30 are in band; 12 do both. Find P(band | sports) as a fraction.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. P(band AND sports) / P(sports) = 12 / 40.
  4. Check the result by substituting or estimating: the response should match 12/40 and make sense in the original problem.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

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
  1. Core Practice: First identify exactly what the question is asking: Same survey. Find P(sports | band) as a fraction.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. P(sports AND band) / P(band) = 12 / 30.
  4. Check the result by substituting or estimating: the response should match 12/30 and make sense in the original problem.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: 12/30

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