Question

probability
the shapes do not have to be the same. for example, the entire region is a rectangle and the target area is a circle.
to find the probability of randomly hitting the target area with a dart, use the geometric probability formula:
$p(a) = \frac{\text{area of target}}{\text{area of entire region}}$ or $p(\text{tam}) = \frac{\text{area of circle}}{\text{area of rectangle}}$
image of a rectangle with target and dimensions 2 cm (vertical) and 5 cm (horizontal) (approximate, as per ocr context)
if the radius of the circle is 2 cm, the base of the rectangle is 8 cm, and the height of the rectangle is 5 cm, what is the probability of hitting the area inside the tan circle? round your answer to the nearest tenth.
a. 96.6%
b. 25.3%
c. 76.1%
d. 31.4%

Explanation:

Step1: Calculate circle area

$A_{circle} = \pi r^2 = \pi (2)^2 = 4\pi \approx 12.566\ \text{cm}^2$

Step2: Calculate rectangle area

$A_{rectangle} = b \times h = 8 \times 5 = 40\ \text{cm}^2$

Step3: Compute probability

$P(\text{hit circle}) = \frac{A_{circle}}{A_{rectangle}} = \frac{12.566}{40} = 0.31415$

Step4: Convert to percentage

$0.31415 \times 100 = 31.4\%$

Answer:

D. 31.4%