Question

Assume that a gallon of milk bought at the store goes bad some time in the interval from 5 days to 10 days after purchase. What is the probability that a randomly chosen gallon of milk goes bad between 6 and 8 days after purchase?

Answer 1

Let's also assume that the probability of the milk going bad is uniformly distributed (you didn't say).

This really has to do with beginning and end of days!

So at the end of day 5 `P(bad)=0` because it certainly survives the first five days.
and after day 10 `P(bad)=1=100%`

The probability of the milk going bad on any day between the beginning of day 6 and the end of day 10 is then `1//5=20%`

"Between 6 and 8 days" means it survives the first 6 days, but will be bad before the end of day 8. Those are two days (during day 7 or 8), so the probability will be `2*1//5=2//5=40%`