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**Len** Suppose that a point $\displaystyle (X_1,X_2,X_3)$ is chosen at random, that is, in accordance with the uniform probability density function over the following set S:

$\displaystyle S = {(x_1,x_2,x_3) : 0 \leq x_1 \leq 1, for i = 1,2,3}$

$\displaystyle

Determine P[(X_1-\frac{1}{2})^2+(X_2-\frac{1}{2})^2+(X_3-\frac{1}{2})^2 \leq \frac{1}{4}$

Not sure how to do this and I have many more similar problems so if someone could give me some help here I may be able to do them all.

Thanks.