A simple dartboard has three areas… the main board has a radius of 11 inches, there is a circle with a radius of 5 inches, and the bullseye has a radius of 2 inches. What is the probability of a random dart landing inside the bullseye? Round to the nearest thousandth.

I believe it is 2/18 or 0.11?? Please help :(

No, you have to do this on the basis of area (which is proportional to radius^2)

pr(bullseye)=(2/11)^2

so it would be 0.0330??

I would have rounded to 0.00331

Rounded to the nearest thousandth -- wouldn't that be 0.033?

yes you are correct Ms. Sue, thank you both :)

You're welcome, Jen.

Oh i forgot to ask....would i use A=Pir^2?

You can use pi r^2 but since you are just taking ratios the pi will cancel.

4 pi/121 pi = 4/121

thank you Damon :)

To find the probability of a random dart landing inside the bullseye, we need to compare the area of the bullseye to the total area of the dartboard.

The total area of the dartboard can be calculated as the area of the main board minus the area of the circle with a radius of 5 inches.

Area of the main board = π * (radius of the main board)^2
Area of the main board = π * (11)^2

Area of the circle with a radius of 5 inches = π * (radius of the circle)^2
Area of the circle with a radius of 5 inches = π * (5)^2

Total area of the dartboard = Area of the main board - Area of the circle with a radius of 5 inches
Total area of the dartboard = π * (11)^2 - π * (5)^2

Now, let's calculate the area of the bullseye, which is a circle with a radius of 2 inches.

Area of the bullseye = π * (radius of the bullseye)^2
Area of the bullseye = π * (2)^2

To find the probability, we divide the area of the bullseye by the total area of the dartboard.

Probability = Area of the bullseye / Total area of the dartboard
Probability = (π * (2)^2) / (π * (11)^2 - π * (5)^2)
Probability = (π * 4) / (π * 121 - π * 25)
Probability = 4 / (121 - 25)
Probability = 4 / 96
Probability ≈ 0.041667

Rounding to the nearest thousandth, the probability of a random dart landing inside the bullseye is approximately 0.042.