Garrett thros a dart at a circular dart board. the dart board has a radius of 16 inches, and the bull's eye in the center of the dart board has a radius of 6 inches. What is the probability that a dart thrown at random within the dartboard will hit the bull's eye?
To find the probability that a dart thrown at random within the dartboard will hit the bull's eye, we need to compare the areas of the bull's eye and the entire dartboard.
The area of a circle can be calculated using the formula: A = πr^2, where A is the area and r is the radius.
Area of the bull's eye:
A_bullseye = π(6^2) = 36π square inches
Area of the entire dartboard:
A_dartboard = π(16^2) = 256π square inches
To find the probability, we divide the area of the bull's eye by the area of the entire dartboard:
P = A_bullseye / A_dartboard = (36π) / (256π) = 36/256 = 9/64 ≈ 0.14
Therefore, the probability that a dart thrown at random within the dartboard will hit the bull's eye is approximately 0.14 or 14%.
To find the probability that a dart thrown at random within the dartboard will hit the bull's eye, we can use the concept of areas.
The area of the entire dartboard is equal to the area of the circle with radius 16 inches. The formula to calculate the area of a circle is A = π * r^2, where A is the area and r is the radius.
Therefore, the area of the dartboard is A_dartboard = π * (16 inches)^2.
The area of the bull's eye is equal to the area of the circle with radius 6 inches. So, the area of the bull's eye is A_bullseye = π * (6 inches)^2.
To find the probability, we can compare the area of the bull's eye to the area of the dartboard. The probability is given by:
P = A_bullseye / A_dartboard.
Substituting the values we have, we get:
P = (π * (6 inches)^2) / (π * (16 inches)^2).
The π (pi) cancels out, so we are left with:
P = (6 inches)^2 / (16 inches)^2.
Simplifying further, we have:
P = 36 / 256.
Thus, the probability that a dart thrown at random within the dartboard will hit the bull's eye is 36/256, or approximately 0.1406, which is equivalent to about 14.1%.
area bulls eye = pi (6^2)
total area = pi (16)^2
6^2/16^2 = 2^2*3^2 /2^8 = 9/2^6 = 9/64
= .140625