calculating the probability of a person having to hold it in, in an office building

[NTShpikho]

the formula: if toilets<ppl: probability= (1- toilets div ppl)*100 else probability = 0;

This formula provides a quick and easy way to estimate the probability of full toilet occupancy based on the number of people and toilets. It assumes that if there are more toilets than people, there will never be full occupancy, which makes sense in practical scenarios.

when ppl outnumber the toilets, as it usually does in office buildings,
complexity rises when taking in to consideration the urgency
of a person to use it.

if the offices serve free milk, the urgency rises exponentially.

this would mean the ppl parameter, is to be replaced by the chance to need a toilet at a given moment: chance;

so the full formula is:

if toilets<ppl: probability= (1- toilets div ppl)*100*chance else probability = 0

and because office building will always have less toilets then employees:
probability=(1- toilets div ppl)*100*chance
where:
chance = toiletBreaksPerHour div (60 div 15)
15 being toilet time or average toilet time on the toilet.