A circular dartboard of radius 1 foot is at a distance of 20 feet from you.…
2026
A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the periphery?
- A.
1/3
- B.
1/2
- C.
3/4
- D.
1/4
Attempted by 4 students.
Show answer & explanation
Correct answer: D
By assuming closer to centre of the circle is less than half the radius and closer to periphery is more than half the radius from centre.
Divide the dart into two concentric circles. Radius of smaller is r/2 and bigger is r.
Dart is closer to centre Q lies in smaller circle.
Probability of point Q lying closer to the centre = (Area of Smaller circle)/(Total area of dart board)
= (π × (r/2)2)/(π r2)
= 1/4