Question

Two congruent circles are inscribed in a trapezoid. Use the drawing at the right to determine the probability of landing in the given region. P(grey region) P(black circle) P(not in black circle)​

Answer 1

P(grey region) = 0.27512

P(black circle) = 0.36243

P(not in black circle) = 0.63757

Explanation:

The circles are congruent and each circle has a diameter of 6 inch

Therefore radius of each circle = 6/2 = 3in

Area of each circle = πr² = π ·3² = 9π = 28.27 square inches

The area of the trapezoid is given by the formula
A = (a+b)/2 x h
where a and b are the top and bottom sides and h is the vertical height

A = (11+15)/2 x 6 = 26/2 x 6 = 13 x 6 = 78 square inches

Area of the grey region - Area of trapezoid - Area of both circles

= 78 - 2(28.27) = 21.46 square inches

P(grey region) = Area of grey region/Area of trapezoid
= 21.46/78

= 0.27512

P(black circle) = Area of black circle/Area of trapezoid
= 28.27 / 78

= 0.36243

P(not in black circle) = 1 - P(black circle)

= 1 - 0.36243

= 0.63757