To solve this problem, we need to find the total area of the composite figure and the area of the semicircular region, and then divide the area of the semicircular region by the total area to get the probability that the randomly selected point is in the semicircular region.
The area of a semicircle with radius r is (1/2)πr^2, and the area of a square with side s is s^2. Therefore, the total area of the composite figure is:
Total area = (1/2)π(5^2) + 10^2 = 25π/2 + 100
The area of the semicircular region is (1/2)π(5^2) = 25π/2.
The probability of selecting a point in the semicircular region is:
Probability = Area of semicircular region / Total area
Probability = (25π/2) / (25π/2 + 100)
Probability = 0.198 (rounded to the nearest tenth)
Therefore, the probability that the randomly selected point is in the semicircular region is approximately 0.2, or 20%.