Probability of 2 real number being between 1/2 and (-1/2)

Question

Got this question on a multiple choice test and had no idea how to solve it.

Q: Let $X,Y,$ and $Z$ be independent random variables uniformly distributed over $(0,1)$. What is $$ \mathbb P\left(|X-Y| < \frac12, |Y-Z|\lt \frac12\right)\quad ? $$ A: $\frac34$

B: $\frac{7}{12}$

C: $\frac 14$

D: $\frac 12$

E: $\frac 23$

Answer 1

Here's your region. You should be able to calculate the volume from this: