Question

1. a point in the figure is selected at random. find the probability that the point will be in the part that is not shaded.

about 20%
about 25%
about 10%
about 5%

Explanation:

Step1: Assume square side length

Let square side = $2r$ (so radius of each circle = $r$). Area of square: $(2r)^2 = 4r^2$.

Step2: Calculate shaded area

4 circles: $4 \times \pi r^2 = 4\pi r^2$.

Step3: Calculate unshaded area

Unshaded = Square area - Shaded area = $4r^2 - 4\pi r^2 = 4r^2(1 - \pi)$.

Step4: Find probability

Probability = $\frac{\text{Unshaded}}{\text{Square}} = 1 - \pi \approx 1 - 0.785 = 0.215 = 21.5\%$.

Step5: Choose closest option

21.5% is about 20%.

Answer:

about 21.5% (closest to about 20%)