Raffle ticket odds, does buying say 10 out of 28,000, give you 1/2800 chance on every ticket or 1/28000?
In: Mathematics
I see a few people saying you’d have a 1/2800 chance to win but actually this is false. Because each ticket that is NOT the winning ticket reduces the overall pool count i.e.
ticket 1 is competing against 27999 tickets but fails to win
ticket 2 is competing against 27998 tickets but fails to win
ticket 3 is competing against 27997 tickets but fails to win etc.
So what you do is you multiply each tickets probability of not winning then subtract that total from 1 to get the probability that you will win.
In this case:
27999/28000 * 27998/28000 * … * 27990/28000 = 0.99803
Then subtract that value from 1.0 which gives you a probability of 0.00197 or 0.197% chance to win given that you bought 10 tickets in a 28000 ticket raffle.
You can use the expected value probability algorithm to calculate other values :).
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