10th grade Geometric probability worksheet

Geometric probability

Grade 10 Math Worksheet

Circle the best answer.

1. Read this first

   Target zones (example figures, made up for practice)

   zone	outer radius (cm)	score
   bullseye	3	10
   middle ring	8	5
   outer ring	12	1

2. 1.

   A beanbag lands at a random spot on Bo's target mat, shown on the card. What is the chance it scores at least 5 points?

   • 4/9
   • 5/9
   • 2/3
   • 55/144
3. 2.

   A beanbag lands at random on Esme's target mat, shown on the card. Given that it scored at least 5 points, what is the chance it hit the bullseye?

   • 9/64
   • 1/16
   • 3/8
   • 55/64
4. 3.

   A bus comes at a random moment within a 30-minute window. Jun asks for the chance the wait is under 10 minutes. Which measure fits, and why?

   • Length: moments are spread along one line of 30 minutes, so use favorable length ÷ total length.
   • Angle: a clock face is round, so compare angles out of 360°.
   • Area: time passes in two directions at once, so compare the areas of the two time spans.
   • No measure works: a chance needs a list of equally likely outcomes to count them one by one in order.
5. 4.

   D and E are the midpoints of sides AB and AC of triangle ABC. A seed lands at a random spot in Kira's triangular garden ABC. What is the chance it lands in triangle ADE?

   • 3/4
   • 1/2
   • 1/3
   • 1/4
6. 5.

   A circle of radius 4 cm is inscribed in Noah's square tile, touching all four sides. A random point is chosen on the tile. About how likely is it to land outside the circle?

   • 1 − π/4 ≈ 0.21
   • π/4 ≈ 0.79
   • 1 − 2/π ≈ 0.36
   • 1 − π/8 ≈ 0.61
7. 6.

   A point (x, y) is chosen at random in the square 0 ≤ x ≤ 6, 0 ≤ y ≤ 6, for Pia's grid game. What is the chance that x + y ≤ 3?

   • 1/8
   • 7/8
   • 1/2
   • 1/12
8. 7.

   A point (x, y) is chosen at random in the square 0 ≤ x ≤ 6, 0 ≤ y ≤ 6, for Ren's grid game. What is the chance that y ≥ 2x?

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

   Two friends arrive at random times between 1:00 and 2:00, each waiting 10 minutes. With x and y minutes after 1:00, which region of the 60 by 60 square means they meet, for Tala?

   • x − y = 10: a single line across the square from edge to edge
   • x ≤ 10 and y ≤ 10: a small square at the corner of the square
   • |x − y| ≤ 10: a band along the diagonal
   • x + y ≤ 10: a small triangle at the corner of the square
10. 9.

    Ari drops a bean at a random spot in a rectangle and asks for the chance it lands in a triangle painted inside. Which measure fits, and why?

    • Angle: a triangle has three angles, so compare the angle measures involved in the shape.
    • Length: the triangle has a base and a height, so compare those two lengths of the shape.
    • Count: the triangle has 3 corners and the rectangle 4, so the chance is 3/4.
    • Area: the bean can land anywhere in a flat region, so use triangle area ÷ rectangle area.
11. 10.

    Two numbers x and y are chosen at random from 0 to 1 for Bo's game. Which region is the event x + y < 1/2, and what is its chance?

    • The triangle under the line x + y = 1/2, with area 1/8, so the chance is 1/8.
    • The triangle under the line x + y = 1, with area 1/2, so the chance is 1/2.
    • The square with x and y each below 1/2, with an area of 1/4, so the chance is 1/4 as well.
    • A line, x + y = 1/2, so the chance is 0 since a line has no area.