Question

Garrett throws a dart at a circular dart board. The dart board has a radius of 15 inches, and the bull’s eye in the center of the dart board has a radius of 2 inches. What is the probability that a dart thrown at random within the dartboard will hit the bull’s eye? Round your answer to the nearest tenth, if necessary.

Answer 1

Area of a circle with radius \(r\): \(A = \pi r^2\)

Find the area of the bull's eye. Find the area of the dart board. The ratio of the areas is the probability that a randomly placed dart will hit the bull's eye.

Answer 2

The answer choices are in % though.
A 1.8%
B 5.6%
C 8.4%
D 13.3%

Answer 3

Okay, multiply the probability (which should be somewhere between 0 and 1) by 100 and tack on a percent sign...

Answer 4

I'm confused. So 15^2pi = about 706.9 and 2^2pi = about 12.6

Answer 5

I know the answer isn't A.

Answer 6

@tcarroll010 Do you know how to solve this?

Answer 7

The P(hitting bull's eye) =

(A)rea of bull's eye divided by (A)rea of dartboard

P = [(pi)(2^2)] / [(pi)(15^2)] = 4 / 225 = (4 / 225) (100) %

Just do the division and you'll get your answer.

Answer 8

All good now, @savannahp8 ?

Answer 9

Wouldn't you have to multiply by pi?
So (706.9/12.6) (100) % = 5.6%
My friend got 1.8% and got it wrong so it must be 5.6%
Right?

Answer 10

pi is in the numerator and the denominator, so it cancels.

P = (4 / 225) (100) % = 1.77777777 %

approx. 1.8 %

You're done!

Answer 11

Good luck to you in all of your studies and thx for the recognition! @savannahp8

Answer 12

np

Answer 13

Yep! Thank you.

Answer 14

uw! Have a good day!

Answer 15

You too!!