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? 84%

50%

42%

16%

Answer 1

[AI-generated answer — Bot GPT 3.5]

The probability that a point chosen inside the larger circle is not in the shaded region is equal to the ratio of the area of the larger circle excluding the shaded region to the total area of the larger circle.

First, we need to find the areas of the circles. The area of a circle is calculated using the formula A = πr^2, where r is the radius of the circle.

For the smaller shaded circle with radius r = 2 inches:
A1 = π(2)^2 = 4π square inches

For the larger circle with radius R = 5 inches:
A2 = π(5)^2 = 25π square inches

The area of the shaded region is A1 = 4π square inches.

The area of the larger circle excluding the shaded region is A2 - A1 = 25π - 4π = 21π square inches.

Therefore, the probability that a point chosen inside the larger circle is not in the shaded region is:
(21π) / (25π) = 21/25 = 0.84 = 84%

So the answer is 84%.