The probability that a point chosen inside the larger circle is not in the shaded region is equal to the area of the larger circle that is not shaded divided by the total area of the larger circle.
The area of the larger circle is πR^2 = π(5)^2 = 25π
The area of the shaded circle is πr^2 = π(2)^2 = 4π
The area of the larger circle that is not shaded is 25π - 4π = 21π
So, the probability is (21π) / (25π) = 21/25 = 0.84 = 84%
Therefore, the probability that a point chosen inside the larger circle is not in the shaded region is 84%.
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? (5 points)
84%
50%
42%
16%
1 answer
5 answers