Question

suppose that all of the points on the circular dartboard shown are equally likely to be hit by a dart. If the radius of the shaded center circle is 2 and the radius of the entire dartboard is 4, what is the probability of throwing a dart and hitting the white part of the board? Round your answer to the nearest whole number.

Answer 1

P(white region) = 0.75 or 75%

Explanation:

Find the area of the shaded region:

A = πr²

A = π(2)²

A = 12.56

Find the area of the entire dartboard:

A = πr²

A = π(4)²

A = 50.24

Find the probability that the dart hits the blue region:

P(blue region) = Area of blue region/ Total Area

P(blue region) = 12.56 / 50.24

P(blue region) = 0.25

As total probability is equal to 1, find the probability of throwing a dart that hits the white part of the board by substracting 0.25 from 1

P(white region) = 1 - P(blue region)

P(white region) = 1 - 0.25

P(white region) = 0.75