Question

The figure below shows a shaded circular region inside a larger circle: A shaded circle is shown inside another larger circle. The radius of the smaller circle is labeled as r and the radius of the larger circle is labeled as R. On the right side of the image is written r equal to 2 inches and below r equal to 2 inches is written R equal to 5 inches. What is the probability that a point chosen inside the larger circle is not in the shaded region? A)84% B)50% C)42% D)16%

Answer 1

Short answer: 84% A
Remark
This sounds like there are only 2 circles that matter. The small one is inside the larger and the small one is shaded.

Step One
Find the area of the small circle.

Givens
r = 2
pi = 3.14

Formula
A = pi*r*r = pi r^2

Sub and Solve
A = 3.14 * 2^2
A = 12.56

Step Two
Find the area of the larger circle
A = pi*r^2
pi = 3.14
r = 5

Area = 3.14 * 5^2
Area = 3.14 * 25
Area = 78.5

Step Three
Find the area of the unshaded region between the larger and smaller circles.

Formula
Area unshaded region = Area of the Large Circle - The area small circle

Givens
Area Large Circle = 78.5
Area Small Circle = 12.56

Solve
Area of unshaded region = 78.5 - 12.56 = 65.94

Find the probability of a point being in the unshaded region.

P(unshaded region) = (Area of Unshaded region / Entire Area)*100%
P(unshaded region) = (65.94 / 78.5) *100%
P(unshaded region) = 84%

Answer: A <<<< 84%

Answer 2

Area of larger circle:  3.14 x 5^2 = 78.5

Area of small circle: 3.14 x 2^2 = 12.56

Difference of the 2 areas: 78.5 - 12.56 = 65.94

Probability of being in large circle but not small circle: 65.94 / 78.5 = 0.84 = 84%


 The answer is A) 84%