Geometric Probability: Analyzing Random Points in Space

A dartboard is circular with a radius of 10 cm. If a dart is thrown randomly at the dartboard, what is the probability that it lands within a smaller circle of radius 5 cm centered at the same point?

• 0.25

• 0.75

• 0.1

• 0.5

A rectangular park measures 100 m by 50 m. If a person randomly walks within the park, what is the probability that they will step on a designated flower bed that occupies an area of 20 m²?

• 0.004

• 0.1

• 0.02

• 0.005

In a square garden with a side length of 20 m, there is a circular fountain with a radius of 4 m in the center. If a person randomly throws a pebble into the garden, what is the probability that it lands in the fountain?

• 0.2

• 0.1256

• 0.1

• 0.05

A circular swimming pool has a diameter of 12 m. If a child randomly swims in the pool, what is the probability that they are within 2 m of the edge of the pool?

• 2/5

• 3/4

• 1/3

• 5/9

A triangular plot of land has vertices at (0,0), (0,6), and (8,0). If a point is chosen randomly within this triangle, what is the probability that the point lies within the area that is closer to the vertex at (0,6) than to the other two vertices?

• 0.5

• 1.0

• 0.75

• 0.25

Tags

CCSS.HSG.GPE.B.7

A rectangular field is 200 m long and 100 m wide. A random point is chosen within this field. What is the probability that the point lies within a circular area of radius 10 m centered at one of the corners of the field?

• 0.0050

• 0.0157

• 0.0250

• 0.1000

Tags

CCSS.HSG.MG.A.2

A circular pizza has a radius of 15 cm. If a slice is cut out that has a central angle of 60 degrees, what is the probability that a randomly chosen point on the pizza is within the slice?

• 1/3

• 1/2

• 1/4

• 1/6

A square plot of land has a side length of 30 m. If a random point is selected within the square, what is the probability that the point is within a smaller square of side length 10 m that is positioned in one of the corners?

• 1/4

• 1/6

• 1/12

• 1/9

A circular track has a radius of 50 m. If a runner randomly selects a point on the track, what is the probability that the point is within 5 m of the starting line?

• 0.5

• 0.01

• 0.1

• 0.25

A rectangular room measures 12 m by 8 m. If a random point is chosen in the room, what is the probability that the point is within a circular rug of radius 2 m placed in the center of the room?

• 0.05

• 0.75

• 0.25

• 0.1309