Question

clarissa and her friends are playing a game by throwing sticky darts onto the board shown below. what is the likelihood of a sticky dart landing in the green section of the board, assuming that the sticky dart lands on the board?

Explanation:

To determine the likelihood of a dart landing in the green section, we assume the dartboard has three concentric circles (let the radii of the green circle, middle circle, and outer circle be \( r \), \( 2r \), and \( 3r \) respectively, as a common setup for such problems).

Step 1: Calculate the area of the green circle

The area of a circle is given by the formula \( A = \pi r^2 \). For the green circle with radius \( r \):
\[ A_{\text{green}} = \pi r^2 \]

Step 2: Calculate the area of the entire dartboard

The entire dartboard is the outermost circle with radius \( 3r \) (assuming the middle circle has radius \( 2r \) and the outer \( 3r \) for a typical 3 - ring setup). Using the area formula:
\[ A_{\text{total}} = \pi (3r)^2 = 9\pi r^2 \]

Step 3: Calculate the probability

Probability is the ratio of the favorable area (green) to the total area (dartboard):
\[ P = \frac{A_{\text{green}}}{A_{\text{total}}} = \frac{\pi r^2}{9\pi r^2} = \frac{1}{9} \]

(Note: If the radii are different (e.g., green radius \( r \), middle \( 2r \), outer \( 3r \) is a common assumption, but if the actual radii from the diagram are different, adjust accordingly. For example, if the green is radius \( r \), middle \( 3r \), outer \( 5r \), the calculation changes. But with the typical 3 - ring setup with radii in ratio \( 1:2:3 \), the probability is \( \frac{1}{9} \).)

Answer:

\(\boldsymbol{\frac{1}{9}}\) (or adjust based on actual radii from the diagram)