Since the radius of the larger circle is 5 inches and the radius of the shaded inner circle is 3 inches, the area of the shaded region can be found by subtracting the area of the inner circle from the area of the larger circle.
Area of larger circle = πR^2 = π(5^2) = 25π square inches
Area of inner circle = πr^2 = π(3^2) = 9π square inches
Area of shaded region = 25π - 9π = 16π square inches
The probability that a point chosen inside the larger circle is not in the shaded region is the ratio of the area not in the shaded region to the total area of the larger circle.
Probability = (Area not shaded) / (Total area) = (25π - 16π) / (25π) = 9π / 25π = 9/25
Converting this to a percentage:
9/25 = 0.36
36%
Therefore, the probability that a point chosen inside the larger circle is not in the shaded region is 36%.
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 3 inches and below r equal to 3 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)
24%
36%
50%
64%
1 answer