If the real numbers x and Y belong to [0,1], then the probability that the square of X + the square of Y is greater than 1 is zero

This is a geometric concept
Make a square with the vertex at the origin, both sides at the X, y positive half axis and the side length of 1
be
X ^ 2 + y ^ 2 = 1 is the unit circle with radius 1
So the probability is the area of the square in the first quadrant minus the area of the unit circle
So probability = 1 - π / 4

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