What is the probability that a randomly thrown dart that lands within the rectangle lands within a shaded region? All of the circles are congruent, and the diameter of each circle is 28 cm. A. 0.112 B. 0.196 C. 0.697 D. 0.785
1) the probability will be equal to the area of the shaded region divided by the area of the rectangle:
                    area of the shaded region probability = -------------------------------------                        area of the rectangle
2) call r the radius of the circles (all are equal)
area of one circle = π (r^2)
area of the four circles = 4Ï€(r^2) = area of the shaded region
3) area of the rectangle
length of the rectangle: 2r height of the rectangle: 8r
area of the rectgangle = (2r)(8r) = 16 r^2
4) probability = 4π(r^2) /[(16)(r^2)] = π / 4
use π = 3.1416
probability = 3.1416 / 4 = 0.785
And you do not need to use the diameter given. The answer does not depend on this number.
