Probability in Shaded Regions Worksheet

Find the probability that a point chosen at random will land in the shaded area. (Refer to the diagram: Rectangle ABCD with a circle of radius 3 centered at E, rectangle dimensions 8 by 6)

• Probability = (Area of shaded region) / (Area of rectangle) = (Area of rectangle - Area of circle) / Area of rectangle = [(8×6) - (π×3²)] / (8×6) = (48 - 28.27) / 48 ≈ 0.41

• Probability = (Area of circle) / (Area of rectangle) = (π×3²) / (8×6) = 28.27 / 48 ≈ 0.59

• Probability = (Area of rectangle + Area of circle) / (Area of rectangle) = (48 + 28.27) / 48 ≈ 1.59

• Probability = (Area of shaded region) / (Area of circle) = (Area of rectangle - Area of circle) / (π×3²) = (48 - 28.27) / 28.27 ≈ 0.70

Find the probability that a point chosen at random will land in the shaded area. (Refer to the diagram: Circle of radius 4 with a sector of 108° shaded)

• 0.3

• 0.15

• 0.5

• 0.6

Find the probability that a point chosen at random will land in the shaded area. (Refer to the diagram: Circle of radius 30 cm with a sector of 50° shaded)

• Probability = (Area of shaded sector) / (Area of circle) = (50/360) × π × 30² / (π × 30²) = 50/360 ≈ 0.14

• Probability = (Area of shaded sector) / (Area of circle) = (30/360) × π × 50² / (π × 30²) = 30/360 ≈ 0.08

• Probability = (Area of shaded sector) / (Area of circle) = (60/360) × π × 30² / (π × 30²) = 60/360 ≈ 0.17

• Probability = (Area of shaded sector) / (Area of circle) = (100/360) × π × 30² / (π × 30²) = 100/360 ≈ 0.28

A dart hits the dart board below.

Find the probability that the dart landed in the shaded region.

(Refer to the diagram: Square dartboard of side 4 m with 4 inscribed circles with radius 1)

• (16 - π) / 16
• (4π) / 16
• (16 - 8π) / 16
• (16 + 4π) / 16
• (16 - 4π) / 16

A dart is thrown at the board below. Find the probability that the dart hit the shaded region. (The board is a square of side 12 units, and the shaded region is formed by subtracting two semicircles from the square.)

• (108 - 36π) / 144
• (144 + 36π) / 144
• (144 - 36π) / 144
• (144 - 18π) / 144

What is the probability of landing in the shaded region? (The board is a square of side 12 cm, with a circle of diameter 8 cm and a horizontal white strip of width 8 cm inside the circle. The shaded region is the area outside the circle but inside the square.)

• (144 - 16π)/144 * 100 ≈ 80.1%
• (144 - 32π)/144 * 100 ≈ 78.5%
• (144 - 16π)/144 * 100 ≈ 64.2%
• (144 - 8π)/144 * 100 ≈ 50.3%