No math here , just cell counting
You're approach is interesting, but I guess it's much
easier with at least a bit of math.
The answer is 1 - (1 - 10/60)^2 = 11/36.
For the other exercise, it was 1 - (1 - 30/120)^2 = 7/16.
I found this by trying and thinking a bit.
As with the other similar exercise, the problem can
be compared with:
If 2 dice are thrown, what is the possibility that at
least one shows a specific number.
In our example with the meeting, it could be translated to
If 2 peeple meet, what is the possibility that at least
one arrives within a range to a specific time (that for
each of them represents the arrival of the other one).
I'm not totally sure with the comparison, but I testet the
formula with the computer for different values and the results