Waiting For The Bus

Calculus Level 3

You arrive at the station at a random time. There are infinitely many buses, but they have very different frequencies of arrival.

Bus 0 comes every minute.
Bus 1 comes every 100 minutes.
Bus 2 comes every 200 minutes.
Bus 3 comes every 300 minutes,
and so on.

To the nearest percent, how likely is it that the first bus to arrive will be Bus 0?

Note: The buses are not synchronized with each other in any way.


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