Question

A circular dartboard has a radius of 2 meters and a red circle in the center. Assume you hit the target at a random point. For what radius of the red center region does P(hitting red) = 0.6?

Answer 1

1.549 m

Step-by-step explanation:

Given:

The radius of the circular board, r = 2 m

The probability of hitting the red is given as 0.6

Now, this probability of hitting the red can be conclude as

0.6 = (Area of red)/ (Total area of the board)

Total area of the board = πr² = π × 2²

let the radius of the red area be R

thus, area of red circle, = πR²

on substituting the value of the area, we have

0.6 = (πR²)/ (π × 2²)

or

R² = 2.4

or

R = 1.549 m

Thus, the radius of the red circle is 1.549 m