Let $W ∼ Uniform[1, 4]$. Compute each of the following. (a) $P(W ≥ 5)$

Question

Let $W ∼ Uniform[1, 4]$. Compute each of the following.

$(a) P(W ≥ 5)$

$$P(W \geq 5) = 1 - P(W < 5)$$

$$=1 - \frac{5-1}{4-1} = 1-\frac{4}{3} = -\frac{1}{3}$$

Answer is $0$. Why? Could someone explain?

Answer 1

By definition of random variable uniformly distributed on $[1,4]$, $W$ can get any value between $1$ and $4$. It is impossible for $W$ to fall outside the interval $[1, 4]$. Therefore, the probability, it got a value larger than $5$, is strictly zero.