The answer is 1/2.
To find P(X ≤ 1 | Y = 1), we need to determine the conditional probability of X being less than or equal to 1 given that Y is equal to 1.
The given triangle with vertices (0, 0), (2, 0), and (1, 2) forms a right triangle. We can see that the line Y = 1 passes through the triangle, dividing it into two smaller triangles.
The triangle with vertices (0, 0), (2, 0), and (1, 1) is the region where Y = 1. This triangle has a base of length 2 and a height of 1, so its area is (1/2) * base * height = (1/2) * 2 * 1 = 1.
The triangle with vertices (0, 0), (1, 1), and (1, 0) is the region where X ≤ 1. This triangle has a base of length 1 and a height of 1, so its area is (1/2) * base * height = (1/2) * 1 * 1 = 1/2.
Therefore, P(X ≤ 1 | Y = 1) is the ratio of the area of the region where X ≤ 1 and Y = 1 to the area of the region where Y = 1:
P(X ≤ 1 | Y = 1) = (1/2) / 1 = 1/2
So, the probability that X is less than or equal to 1 given Y is equal to 1 is 1/2.