What is the probability of a randomly tossed bean bag landing in the yellow target area? Gray is 2m and yellow 0.75m
Use 3.14 for pi and round to nearest whole percent.
A. 38
B.14
C.36
D.3
Are those measurements diameters or radii?
Is the yellow area inside the gray area?
ANswer it !
To calculate the probability of a randomly tossed bean bag landing in the yellow target area, we need to compare the areas of the gray and yellow regions.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius of the circle.
Given that the radius of the gray circle is 2m, we can calculate its area:
A_gray = 3.14 * (2m)^2 = 12.56 square meters
Given that the radius of the yellow circle is 0.75m, we can calculate its area:
A_yellow = 3.14 * (0.75m)^2 = 1.7675 square meters (rounded to 4 decimal places)
Now, to find the probability of landing in the yellow target area, we divide the area of the yellow region by the area of the total region (gray + yellow):
P_yellow = (A_yellow / (A_gray + A_yellow)) * 100
Substituting the values:
P_yellow = (1.7675 / (12.56 + 1.7675)) * 100
P_yellow = (1.7675 / 14.3275) * 100
P_yellow = 0.1231 * 100 ≈ 12.31% (rounded to 2 decimal places)
Since we need to round to the nearest whole percent, the probability of a randomly tossed bean bag landing in the yellow target area is approximately 12%. Therefore, the answer is B. 14.