At work there is a Grand National (horse racing) Sweepstake Competition.

Rules of the Sweepstake:

there are 40 tickets, each ticket is assigned to a horse (not assigned yet), you can buy maximum of 2 tickets, all tickets must be sold, who ever holds the ticket with the number assigned to the winning horse wins

My Question:

Based on the rules of the sweepstake described above if i wait for a certain number of tickets to be sold before buying my ticket does this affect my odds of winning? if so when would be the optimum time to pick a ticket i.e. after how many tickets sold should I buy my ticket to have the best chance of winning

My thinking:

I assume it does because if there was 100 tickets 99 losers and 1 winner and some one else buys one then statistically the chances of them picking the winning ticket is low (1/100) so if you pick next chances are, your now picking out 98 losing tickets and 1 winner so your chances are now 1/99 (minus the chance of the 1st person picking the winning ticket) I know that this sort of basic intuitive thinking is usually wrong when it come to statistics and probability.


The time of buying has no influence whatsoever.

The chance to pick the winning ticket is given by


with $N$ being the overall number of tickets and $M$ being the number of tickets already drawn. $\frac{N-M}{N}$ is the chance, that the winning ticket has not yet been sold.


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