Suppose train on line A arrives in time uniformly distributed between 0 and 4mins, train on line B arrives in time uniformly distributed between 0 and 6 mins, and furthermore the time interval between A and B arrival is uniformly distributed between 0 and 4.
a. What is the probability train on line A arrives first
b. What is the probability you wait less than 2 mins for one of the trains to arrive.
Here's how I approached this question,
Let $A : $ arrival time for train on line A $\sim U(0,4)$, $B : $ arrival time for train on line B $\sim U(0,6)$
and it is given that $A-B \sim U(-4,4)$
a. $P(A<B) = P(A-B<0) = \frac{1}{2}$
b. This is where I'm stuck, $P(\mathrm{min}(A,B) \leq 2) = 1 - P(A>2, B>2)$
But I'm not sure how I'd go about computing $P(A>2, B>2)$ any help or hint is appreciated, thanks.