# Calculate $P(|X-4| > 1.5)$

If $X \sim U(2, 8)$

Would it be $$P(X > 1.5 + 4) + P(X <-1.5 +4)$$

• Yes, you are correct! – SWilliams Jun 14 '15 at 23:13

$$\begin{split} P(\left| X-4 \right|) > 1.5) &= P(X > 5.5) + P(X < 2.5) \\ &= \frac{2.5}{6} + \frac{0.5}{6} \\ &= \frac12 \end{split}$$