I'm trying to keep the question short. Today the teacher said something like this.Your chance of winning in the national lottery does not depend on which city you bought the ticket from. If you want, buy your ticket from city "A" or buy your ticket from city "B". Your probability of winning does not change.A criticism was made to the teacher: But the people who win are always those who live in city "A". The teacher replied as follows. Because the number of tickets sold in city "A" is more than the number of tickets sold in city "B". However, no matter which city you buy a ticket from, your chances of winning will always remain the same.After some thought, I made an objection.
I said, this argument is valid only and only if:
If the number of tickets DISTRIBUTED to be sold to city "A" and "B" is the same, then my chances of winning will not change. Then, the probability of winning for people living in city "A" may be attributed to the over-selling of tickets. But even this argument is not valid if the winning ticket should only have $1.$ Because the number of distribution and purchase of the ticket to cities is not the same thing.
My question: Is the teacher right? What am I getting wrong? Where am I making a mistake?