Suppose that a point (X1, X2, X3) is chosen at random, that is, in accordance with the

Question:

Suppose that a point (X1, X2, X3) is chosen at random, that is, in accordance with the uniform p.d.f., from the following set S:
S = {(x1, x2, x3): 0 ≤ xi ≤ 1 for i = 1, 2, 3}.
Determine:
a. Pr[X1 – 1/2)2 + (X2 – 1/2)2 + (X3 – 1/2)2 ≤ 1/4]
b. Pr(X21 + X22 + X23 ≤ 1)