Train arrival Paradox

Question

I am unable to understand the solution to this question: "At your subway station, you notice that of the two trains running in opposite directions which are supposed to arrive with the same frequency, the train going in one direction comes first 80% of the time, while the other train going in the opposite direction comes first 20% of the time. What do you think could be happening?

The solution provided is: " Assume that your arrival in the station is uniformly distributed. If both trains run every ten minutes and train A comes into the station at 1, 1:10, 1:20,..while train B comes at 1:12, 1:22, ..then train A will come first 80% of the time." I don't understand the logic here.

Answer 1

If the ones digit of the minutes of your arrival is 0 or 1, then you see the B train first. If the ones digit of the minutes of your arrival is 2, 3, 4, 5, 6, 7, 8, 9, then you see the A train first.

Your arrival time is uniformly distributed...

Answer 2

Suppose the eastbound train arrives at 2:00 and then the westbound train at 2:01.

Then the eastbound train arrives at 3:00 and then the westbound train at 3:01.

Then the eastbound train arrives at 4:00 and then the westbound train at 4:01.

Then the eastbound train arrives at 5:00 and then the westbound train at 5:01.

And so on.

Is there anything in this that implies they don't arrive with equal freqencies --- once per hour?

Now add a bit of randomness so that occasionally --- say $20\%$ of the time, the westbound train arrives first.

Answer 3

In every slice of 10 minutes, for 2 minutes (say 1:00 to 1:02) the train to arrive is A, and for the next 8 minutes (say 1:02 to 1:10), the train to arrive is B.

The probabilities are 2/10 for A and 8/10 for B.