# Office Sweep Probability when buying multiple tickets

With the world cup coming up, our office/yard is having an office sweep. Each person who buys a ticket randomly draws a team out of a hat/box. Because we don't have 32 people in these locations, generally the office people buy two random tickets then the people in the yard buy a single random ticket.

Let's assume 8 teams are more likely to win than the others, is there any difference in the odds of winning if:

A) The office people buy two tickets than the yard buy the remaining.

B) The office people buy a single ticket, than the yard people buy a single ticket, than the office buy another ticket.

I feel like the odds should change, because there is then less choices for the yards people in A.

I understand obviously the office staff have an advantage because they are buying two tickets. But does the order of buying them affect chances?

Since each ticket has the same probability of being the winning ticket, the order of choosing doesn't matter. A person who buys $2$ tickets has a probability of $\frac{1}{16}$ of winning, no matter when he buys the tickets. Since all the tickets are drawn at random, the last ticket is just as likely to win as the first.
• @Phalanx Then obviously it is advantageous to be one of the first $8$ people who chooses. I would think that choosing early in the process would be more important than the number of tickets you get to buy, but in any event it wouldn't be fair to let the people who choose early also buy two tickets at that time. – saulspatz Jun 13 '18 at 0:06