A point (x, y) is to be selected from the square S containing all points (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Suppose that the probability that the selected point will belong to each specified..

Question

A point (x, y) is to be selected from the square S containing all points (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Suppose that the probability that the selected point will belong to each specified subset of S is equal to the area of that subset. Find the probability of each of the following subsets:

(a) the subset of points such that (x − 1/2)^2 + (y−1/2)^2 ≥1/3

(b) the subset of points such that 1/2 < x + y < 5/2

(c) the subset of points such that y ≤ 1 − ^3

(d) the subset of points such that x = y

Answer 1