Question

Shown in the picture below are three concentric (having the same

center) circles. Let's name them small, larger and largest. You are
blindfolded and throwing a dart at the target. What is the probability
that the dart will hit the white area inside the circles? The white area
is formed by the small circle and by the area between the larger and
largest circles that looks like a ring. Assume that the dart you throw,
will hit somewhere inside the largest circle,
Enter your answer as a decimal.

Answer 1

The probability that the dart will hit the white area is 16/25

Explanation:

The given circle is composed of three concentric circles as follows;

Small circle with radius, r₁ = 1

Larger circle with radius, r₂ = 3

Largest circle with radius, r₃ = 5

The area of the small circle = π × r₁² = π

The area of the larger circle = π × r₂² = π × 3² = 9·π

The area of the largest circle = π × r₃² = π × 5² = 25·π = The total target area

The total white area = The total target area - The area of the larger circle

The total white area = 25·π - 9·π = 16·π

The probability of hitting the white area = 16·π/25·π = 16/25

Therefore, the probability that the dart will hit the white area = 16/25.