You are not more likely to arrive at one of the smaller gaps because there are more of them; you seem to think that there is some sort of urn from which you are drawing out gaps of time with equal probability; easy mistake to make. Think of it this way; you are minutes from an urn, numbered :00-:59. There is one 45 minute gap and 15 one -minute gaps. You are most likely to pick a minute belonging to the 45 minute gap.

Additionally, what he says doesn't apply to all non-uniform distributions, but only to those where the times between buses are exponentially distributed (and thus memoryless)

## Do agree

You are not more likely to arrive at one of the smaller gaps because there are more of them; you seem to think that there is some sort of urn from which you are drawing out gaps of time with equal probability; easy mistake to make. Think of it this way; you are minutes from an urn, numbered :00-:59. There is one 45 minute gap and 15 one -minute gaps. You are most likely to pick a minute belonging to the 45 minute gap.

Additionally, what he says doesn't apply to all non-uniform distributions, but only to those where the times between buses are exponentially distributed (and thus memoryless)