Small question on exponential distribution
Let $X$ be a random variable and the duration of a phone call. We know that already $1$ minute has passed. How big is the probability that the phone call goes on for $3$ additional minutes? The CDF is $$F(x)=1-e^{(-1/4\cdot x)}$$
So my thought is to use the formula for the conditional probability:
$$P(X \ge 4 | X > 1) = \frac{P(X \ge 4 \cap X > 1)}{P(X > 1)}$$
I know that $P(X > 1)= e^{(-1/4)}$ but I'm not sure how to compute $P(X \ge 4 \cap X > 1)$. Is this the same probability as $P(X\ge4)$? I mean if $4$ minutes pass, this also implies that $1$ minute has passed.
$P(X \geq 4 \cap X>1) = P(X \geq 4)$ since $\{X \geq 4\} \subset \{X >1\}$.