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Annette [7]
3 years ago
11

John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere o

n 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%

Mathematics
1 answer:
yulyashka [42]3 years ago
3 0

Answer:

Probability = 51\%

Step-by-step 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 = \frac{78.5}{153.86}

Probability = 0.51020408163

Convert to percentage

Probability = 0.51020408163 * 100\%

Probability = 51.020408163\%

Approximate

Probability = 51\%

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