Question

John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere on the board, what is the probability that the thumbtack will be placed on the inner circle? Use 3.14 for , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%

Answer 1

`Probability = 51\%`

Explanation:

Given

Radius of inner circle = 5ft

Radius of outer circle = 7ft

Required

Determine the probability that the thumbtack will be placed on the inner circle

We start by calculating the area of both circles;

Inner Circle

`Area = \pi r^2`

`Area = 3.14 * 5^2`

`Area = 3.14 * 25`

`Area = 78.5`

Outer Circle

`Area = \pi R^2`

`Area = 3.14 * 7^2`

`Area = 3.14 * 49`

`Area = 153.86`

At this point, the probability can be calculated;

The probability = Area of Inner Circle / Area of Outer Circle

`Probability = (78.5)/(153.86)`

`Probability = 0.51020408163`

Convert to percentage

`Probability = 0.51020408163 * 100\%`

`Probability = 51.020408163\%`

Approximate

`Probability = 51\%`