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 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?

24%
36%
50%
64%

Answer 1

Probability is 64%

Explanation:

Given the smaller circle which is shaded whose radius is denoted by r and the largest circle whose radius is denoted by R

r = 3 inches

R = 5 inches

Step 1 : To calculate the area of shaded region.

Area of circle =
`\pi\cdot r^(2)`

⇒ Area =
`(22(3)(3))/(7)`

=
`(198)/(7)` square inches

Step 2 : To calculate the area of larger circle.

Area of circle =
`\pi\cdot r^(2)`

⇒ Area =
`(22(5)(5))/(7)`

=
`(550)/(7)` square inches

Step 3 : Calculate the probability that a point chosen from shaded region

Probability = Area of shaded region/Area of larger circle.

=
`(198)/(7)`/
`(550)/(7)`

=
`(198)/(550)`

= 0.36 = 36%

Step 4 : calculate the probability that a point chosen inside the larger circle is not in shaded region.

Probability = 1 - 0.36

= 0.64 = 64%

Hence the probability is 64%