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?

   • 1/4
   • 1/2
   • 9/16
   • 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?

   • 25/36
   • 1/3
   • 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?

   • 1/4
   • 3/4
   • 1/2
   • 1/3
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/6 ≈ 0.52
   • π/12 ≈ 0.26
   • 1 − π/6 ≈ 0.48
   • 1/6 ≈ 0.17
5. 5.

   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?

   • 1/8
   • 1/4
   • 1/2
   • 3/4
6. 6.

   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
   • 1 − 3√3/(4π) ≈ 0.59
   • 3√3/(2π) ≈ 0.83
7. 7.

   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/(6√3) ≈ 0.30
   • π/(2√3) ≈ 0.91
   • π/4 ≈ 0.79
8. 8.

   Zee's square card has side 10 cm, corner A and center O. A random point P is chosen on the card. What is the chance P is closer to A than to O?

   • 1/2
   • 7/8
   • 1/4
   • 1/8

9. Read this first

   Game target (example figures, made up for practice)

   zone	outer radius (cm)	prize (points)
   bullseye	3	15
   middle ring	6	3
   outer ring	9	0

10. 9.

    A beanbag lands at a random spot on Ari's game target, shown on the card. A toss costs 2 points and pays the prize points for its zone. What happens to a player on average?

    • Loses about 0.67 points per toss
    • Gains about 0.67 points per toss
    • Gains about 1.00 point per toss
    • Gains 4.00 points per toss
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.
    • No: the chance becomes 8 times as large, because the radius is used three times.
    • 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.