Hello mathemagicians,
We have this drawing for free tickets at my workplace and it just so happens that the same person has won twice in a row and this person has a close personal relationship with the raffle-drawer. I strongly suspect that the "random" raffle is not so random, but just to satisfy my own personal curiosity about how low the chances of this person winning twice in a row is I'd like to do the math but I ran into a snag, with which I'd like your help.
I'm trying to calculate the odds of this person winning twice in a row.
The first drawing had 31 entrants. All entrants have 1 ticket. 2 winners are drawn from this pool.
The second drawing had 25 entrants. All entrants, again, have 1 ticket. 1 winner is drawn from this pool.
What are the odds of this person winning both the first drawing and second drawing? I know it's not as straightforward as $\frac{1}{31}\ast\frac{1}{25}$ but I don't know how to transform the first probability to accurately capture the two drawings for two winners.
Thanks for your advice & expertise.
Best Answer
We might also consider what is the chance that someone (not a specific individual chosen in advance) wins twice in a row. This is a bit tricky since there are different numbers of entrants. But assuming that all $25$ people in the second contest were also in the first contest, the probability of someone winning both times is
$$1-\left(\frac{773}{775}\right)^{25}\approx .0626$$
So there is about a $6\%$ chance that someone would win twice in a row.