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 25%
about 50%
about 65%
about 40%

Explanation:

Step1: Assume circle radius r

Let radius of each circle = \( r \). Area of one circle = \( \pi r^2 \), 4 circles total shaded area (approx, accounting for overlaps) ≈ \( 3.2\pi r^2 \) (overlaps reduce total shaded area).

Step2: Calculate total figure area

Total figure width ≈ \( 4r \), height ≈ \( 2r \), area ≈ \( 8r^2 \).

Step3: Compute unshaded probability

Unshaded area = Total area - shaded area ≈ \( 8r^2 - 3.2\pi r^2 ≈ 8r^2 - 10.05r^2 \)? Correction: Better visual estimate—unshaded region is ~2/5 of total, so ~40%.

(Note: Visual probability problems rely on estimating unshaded proportion; ~40% matches the option.)

Answer:

about 40%