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Grade 10 · Math · Geometry

10th grade Geometric probability worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Geometric probability

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. Bo cuts a 15-ft rope at a random point. What is the chance both pieces are at least 4 ft long?

    • 7/8
    • 11/15
    • 8/15
    • 7/15

  2. A bus comes every 20 minutes. Esme arrives at a random time. What is the chance of waiting more than 5 minutes?

    • 1/4
    • 3/4
    • 3/5
    • 1/3

  3. Jun's 60-minute show has one ad at a random minute. What is the chance the ad is in the first 15 minutes or the last 10 minutes?

    • 7/12
    • 5/7
    • 1/4
    • 5/12

  4. Kira's yard is 8 m by 10 m, with a 3 m by 4 m sandbox. A ball lands at a random spot in the yard. What is the chance it lands in the sandbox?

    • 17/20
    • 3/17
    • 3/20
    • 7/18

  5. Luz's target mat is a circle of radius 10 cm, and the bullseye has radius 2 cm. A beanbag lands at a random spot on the mat. What is the chance it hits the bullseye?

    • 24/25
    • 1/5
    • 1/24
    • 1/25

  6. A seed lands at random in Milo's 12 m by 8 m park, which has a triangular bed (base 6 m, height 4 m). What is the chance it lands in the bed?

    • 1/7
    • 1/4
    • 7/8
    • 1/8

  7. Noah's spinner has a red sector of 72° and a blue sector of 90°. The rest is white. The arrow stops at a random spot. What is the chance it stops on white?

    • 9/11
    • 9/20
    • 11/20
    • 4/5

  8. Pia's square park has 10 m sides and a round pond of radius 3 m. A raindrop lands at random in the park. Which calculation gives the chance it lands in the pond?

    • π × 3 ÷ 10
    • π × 3² ÷ (10² − π × 3²)
    • 2π × 3 ÷ (4 × 10)
    • π × 3² ÷ 10²

  9. Ren's round target has outer radius 8 cm and an inner circle of radius 5 cm. Which calculation gives the chance a random beanbag lands in the outer ring only?

    • (8 − 5)² ÷ 8²
    • 5² ÷ 8²
    • (8 − 5) ÷ 8
    • (8² − 5²) ÷ 8²

  10. A class lasts 50 minutes. Tala's fire drill starts at a random minute. Which calculation gives the chance it starts between minute 10 and minute 30?

    • 30 ÷ 50
    • 20 ÷ (50 − 20)
    • (50 − 20) ÷ 50
    • (30 − 10) ÷ 50
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10th grade Geometric probability worksheet – printable
Print: 123456

About this worksheet

Geometric probability: chances from lengths and areas. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can set up a chance as part ÷ whole for lengths, areas and angles, including a window on both sides of a point.
  • I can find the chance for a ring, a triangle inside a larger triangle, an inscribed shape, a region cut by a line, or two random times, and judge a score in the long run.
  • I can work back from a chance to a radius, and check a claim about doubling a radius.

Standard: no CCSS standard names it (S-CP.A.1 and G-MG.A.1 related)

Words to know

random spot: Every point is just as likely as every other point.

piece ÷ whole: The chance: the size of the target part over the size of everything.

region: The flat shape where the point can land.

central angle: The angle at the center of a spinner, out of 360°.

ring: The part between two circles that share a center.

Common mistakes

Your child counted a window on only one side. When a region has two ends or two sides, add them before dividing by the whole.

Your child found the chance of the opposite event. Check whether the question asks for the event or for its opposite.

Your child compared the part to the rest instead of to the whole. A chance is part over whole.

Questions parents ask

What is the most common mistake with geometric probability?

Your child counted a window on only one side. When a region has two ends or two sides, add them before dividing by the whole.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

See all Geometry

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