A simple dartboard has three areas the main board has a radius of 9 inches there is a circle with a radius of 5 inches ans the bullseye has a radius of 3 inches What is the proability of a random dart landing inside the bullseye Round to the nearest 1000th
I am assuming that you you disregarding any skill factor involved and you are certain that the dart will land randomly inside the circle.
Area of whole circle = π(81) = 81π
area of inner circle = π(9) or 9π
prob of landing in inside circle = 9π/(81π) = 1/9 or .11
To find the probability of a random dart landing inside the bullseye, we need to compare the area of the bullseye to the area of the entire dartboard.
First, let's calculate the area of the bullseye. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
The radius of the bullseye is given as 3 inches, so the area of the bullseye is:
A_bullseye = π * (3 inches)^2
A_bullseye ≈ 3.14159 * (3 inches)^2
A_bullseye ≈ 3.14159 * 9 square inches
A_bullseye ≈ 28.27431 square inches (rounded to 5 decimal places)
Next, let's calculate the area of the entire dartboard, which consists of the main board and the circle around it.
The radius of the main board is given as 9 inches. So, the area of the main board is:
A_main = π * (9 inches)^2
A_main ≈ 3.14159 * (9 inches)^2
A_main ≈ 3.14159 * 81 square inches
A_main ≈ 254.469 square inches (rounded to 3 decimal places)
The circle around the main board has a radius of 5 inches. So, the area of this circle is:
A_circle = π * (5 inches)^2
A_circle ≈ 3.14159 * (5 inches)^2
A_circle ≈ 3.14159 * 25 square inches
A_circle ≈ 78.539 square inches (rounded to 3 decimal places)
Now, to find the total area of the dartboard, we add the areas of the main board and the circle:
A_total = A_main + A_circle
A_total ≈ 254.469 square inches + 78.539 square inches
A_total ≈ 332.008 square inches (rounded to 3 decimal places)
Finally, we can calculate the probability of a random dart landing inside the bullseye by dividing the area of the bullseye by the total area of the dartboard:
Probability = A_bullseye / A_total
Probability ≈ 28.27431 square inches / 332.008 square inches
Probability ≈ 0.085355 (rounded to 6 decimal places)
Therefore, the probability of a random dart landing inside the bullseye is approximately 0.085 (rounded to the nearest thousandth).