> It feels contradictory for P(you win the same lottery twice) $\neq$
P(you win the same lottery twice|you won the lottery once).
Would you expect P(you win the lottery exactly zero times) = P(you win the lottery exactly zero times | you won the lottery once)?
> Intuitively, why aren't these two probabilities equal?
There are at least two ways of looking at it.
1. P(you win the same lottery twice|you won the lottery once) is a simpler case than most conditional probabilities. It can be straightforwardly rephrased as P(you win the lottery for a second time).
2. Conditional probability always excludes some possibilities. The possibility that you never win the lottery must be taken into account when calculating P(you win the same lottery twice) but it must be ruled out when calculating P(you win the same lottery twice|you won the lottery once).
Peter Taylor
·
2023-04-25T07:09:03Z (12 months ago)