“I’m not sure why people have introduced multiplication. This would result in the odds of acceptance at all ten schools (one in ten billion under a 10/10% scenario). To arrive at a figure that would represent the chances of getting into at least one school (76% under the same simplified assumptions), the relevant math is essentially additive.”
@merc81 No, the probability of getting into at least one if the probability of getting into each is x%, and the n variables are independent is y = 1 - (1-x)^n. In other words multiplying the probability of not getting into each school. If x=10% and n=10 then the result y is 65%. In the limit as x tends to zero then y tends to n * x which I guess is where your “essentially additive” comes from.
But the point is that these variables are not independent so you can’t multiply them.