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 pi , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%

Answer 1

Answer: A. 51%

Explanation:

Area of circle =
`\pi r^2` , where r = radius of the circle.

In the figure below, we have the complete question.

According to that,

Radius of outer circle = 7ft

Radius of inner circle = 5ft

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

`=\frac{\text{Area of inner circle}}{\text{Area of outer circle}}\\\\=(\pi (5)^2)/(\pi (7)^2)\\\\=(25)/(49)`[π is canceled from numerator and denominator

in percent,
`(25)/(49)*100=51.0204081633\%\approx51\%`

So, the probability that the thumbtack will be placed on the inner circle = 51%

Hence, the correct option is A. 51%.