> The second sentenxe doesn't follow the first - it's a flavor of Zeno's paradox, after 5 years, you'll be left with 4/5 x 4/5 x 4/5 x 4/5 x 4/5 of the original batch.
You made a mistake: it's not that 1/5 of the computers spontaneously break every year. It's that 1/5 of the students treat their computers roughly.
Assuming that laptops get collected over the summer and re-distributed each year, you should actually expect that 100% of each tranche of laptops would need to be replaced every 5 years.
I don't understand how that math could work. Assuming random assignment, the probability that a given computer is given to a one of those students is identical from year to year.
> I don't understand how that math could work. Assuming random assignment, the probability that a given computer is given to a one of those students is identical from year to year.
That's fair. I guess, it's more accurate to say that you'd expect a number of laptops equal to the size of the initial tranche to be destroyed after the first 5 years.
Although if I was running IT, it'd definitely keep track of the "destructive" students and issue them the oldest equipment, in which case, we'd be back to something closer to my original statement.
You made a mistake: it's not that 1/5 of the computers spontaneously break every year. It's that 1/5 of the students treat their computers roughly.
Assuming that laptops get collected over the summer and re-distributed each year, you should actually expect that 100% of each tranche of laptops would need to be replaced every 5 years.