Geometric probability

Grade 10 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   Esme and a friend each arrive at a random time between 1:00 and 2:00. Each waits 15 minutes for the other, then leaves. What is the chance they meet?

   • 1/2
   • 9/16
   • 1/4
   • 7/16
2. 2.

   Jun and a friend each arrive at a random time between 3:00 and 5:00. Each waits 20 minutes for the other. What is the chance they meet?

   • 1/3
   • 25/36
   • 11/36
   • 1/6
3. 3.

   Kira tosses a beanbag onto a circular mat of radius 10 cm. What is the chance it lands closer to the center than to the edge?

   • 1/2
   • 3/4
   • 1/3
   • 1/4
4. 4.

   Luz's 12 cm by 8 cm card has a quarter-circle sticker, radius 4 cm, at each corner. A bead lands at random on the card. About how likely is it to hit a sticker?

   • π/12 ≈ 0.26
   • 1/6 ≈ 0.17
   • 1 − π/6 ≈ 0.48
   • π/6 ≈ 0.52
5. 5.

   P is a random point inside square ABCD with side 10 cm, for Milo's puzzle. What is the chance that angle APB is greater than 90°?

   • π/16 ≈ 0.20
   • π/4 ≈ 0.79
   • 1/2 = 0.50
   • π/8 ≈ 0.39

6. Read this first

   Target zones (example figures, made up for practice)

   zone	outer radius (cm)	score
   bullseye	2	20
   middle ring	6	5
   outer ring	10	1

7. 6.

   A beanbag lands at a random spot on Noah's target mat, shown on the card. What is the average score per toss in the long run?

   • 3.04 points
   • 8.67 points
   • 6.40 points
   • 3.60 points
8. 7.

   A beanbag lands at random on a circular mat of radius 10 cm. Pia learns it landed on the right half. Given that, what is the chance it is within 5 cm of the center?

   • 1/2
   • 3/4
   • 1/4
   • 1/8
9. 8.

   An equilateral triangle is inscribed in a circle of radius 6 cm. A random point is chosen in Ren's circle. About how likely is it to lie inside the triangle?

   • 3√3/(4π) ≈ 0.41
   • √3/(4π) ≈ 0.14
   • 3√3/(2π) ≈ 0.83
   • 1 − 3√3/(4π) ≈ 0.59
10. 9.

    Tala's tile is a regular hexagon with 6 cm sides and an inscribed circle touching each side. A random point lands on the tile. How likely is it to be in the circle?

    • 1 − π/(2√3) ≈ 0.09
    • π/(2√3) ≈ 0.91
    • π/(6√3) ≈ 0.30
    • π/4 ≈ 0.79
11. 10.

    Bo says doubling the radius of a target mat's bullseye doubles the chance of hitting it, if the board stays the same. Which verdict is right?

    • No: the chance becomes 4 times as large, because area depends on the square of the radius.
    • Yes: the chance depends on the radius, so doubling it doubles the chance.
    • No: the chance becomes 3 times as large, because the new area adds 2 more copies.
    • No: the chance becomes 8 times as large, because the radius is used three times.