> After the first year, about 1/5 laptops needed major repair. None of them would make it to 5 years.
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.
> 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're assuming that 4/5 of the laptops remained in pristine condition. I doubt that very much. You need to take account for the ordinary wear and tear compounded together with the impact of abusive 1/5 of users that do an excessive amount of damage (requiring a total overhaul.)
And anyway, if 1/5 of laptops needed major repairs and some of them got it, those go back into circulation. Are they still original laptops? (Ask my grandfather's axe...)
It's not the case that there's a constant 1/5 probability of failure each year. Many failure modes are based on cumulative stress/degradation; so the probability of failure can go up over time.
Some failure modes go down over time; maybe there's some manufacturing defect, and those that have the defect fail early, while those that survive past the first year will have lower chances of failure early on.
But in this kind of environment, the cumulative stresses are much more likely than the early failures.
This was the case. There were no pristine laptops. Some kids are gentle with them, but things happen outside their control, kids play destructive pranks, or are just clumsy. Theoretically possible to make it to 5 years? Sure. Practically? No.
On the other hand, considering we are talking about kids breaking laptops, this failures are much more random, a brand new laptop is not that much more likely to survive a fall than an old one.
All data you have from the author's sentence is the first year, none about the following ones, then the conclusion that none last the full five years. But you assumed it's 1/5th per year, every year.
Anyway, it doesn't matter much either way, even if there's a few that survive, they will be having wear and tear to the point you wouldn't want another student to have them (or maybe as a replacement for a broken one); you wouldn't want some year 1 students to get a new ones while others get the year 4/5 leftovers, they'll resent it for sure.
For things which are effectively integers there is no paradox when your division results in a number less than one you have nothing or perhaps more accurately a probability of having 1 but any given instance in actuality has either 1 or zero. Also equipment failure isn't a linear thing its a curve as things reach expected lifespan. For instance a battery which is nontrivial to replace has an expected number of charge cycles until your battery is so shot you can't really use it off a charger any longer. An increasing number of mechanical hard drives fail, charger sockets start failing. Heating and cooling cycles cause progressive degradation of electronics.
You absolutely could design it to last 20 years with batteries that are easy to pop out and pop in as easy as changing a double aa but your customers won't pay a premium over a more disposable machine and indeed if your customer has a good experience over the 3-5 they actually use it for you make MORE if your hardware is designed to need replacement.
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.