Ah I see, further work needed...

Also the "Geometry" tag might be helpful.

They don't necessarily arrive on the minute intervals. Your calculation is approximately correct, but not accurate enough.

To the serial downvoter, I will find out who you are, do worry about it.

Montecarlo is meant to time out. You need a more optimised solution. It doesn't hurt learning about Bayesian Statistics.

I assume I am missing something but I'm confused by the 18.75 value for the example. The boy arrives from 07:55 to 08:01 which is 7 different arrival times (55, 56, 57, 58, 59, 00, 01), the bus arrives between 07:58 and 08:02 giving 5 different arrival times (58, 59, 00, 01, 02). Therefore there are 7*5=35 total scenarios, of which 6 mean he will miss the bus:
boy arrives at 07:59, bus arrives at 07:58,
boy arrives at 08:00, bus arrives at 07:58 or 07:59,
boy arrives at 08:01, bus arrives at 07:58, 07:59, or 08:00
So 6 misses out of 35 total scenarios is 17.14% ?
What am I missing?