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JPryde's Avatar

01.27.2014 , 04:50 AM | #4
No, part 2 unfortunately is tricky.

We got 15 winners to find.

First winner is easy... it is simply 1-995/1000 for the player (5 tickets) and if that fails, some other guy won, who had 3,5 tickets on average... being 1-x.

From second draw on, there is a chance, that a previous winner wins again, which would result in another draw. On Stage 1, we had 15 draws, flat and square. On Stage 2, we could have a lot more draws, cause each duplicate would result in another draw. But we do not know how many draws exactly it will be, we only know that there are roughly 285 players (1 + 1000/3.5) each holding 1-x tickets (avg. 3.5)

Your equation is easily to be falsified, as the chance to win on stage 2 obviously is higher than on stage 1, not lower. The chance to get drawn "directly" is as high as on stage 1... .but additionally each ticket can win on the "secondary" draw, when a winner wins again.... so the chance to win on stage 2 is higher than on stage 1... 5% cannot possibly be right.

Unfortunately, the possible variations of tickets on players are near endless... for example, 1000 tickets could be distributed as follows:
5 player, 712 on player 2 and 1 ticket each on player 3 through player 285 (this would be an average of 3,5035 still). That however would mean, that we got a really big chance of duplicates, as player 2 got over 70% chance to win the first ticket and still over 70% to get another ticket drawn of his.... this is easily more than if every player had indeed 3 or 4 tickets. (the avg is the same with distributing halve 3 and half 4 tickets, but the chance for a duplicate is a lot less.)
In fact we do not even know the numer of other players. The distribution of tickets is indeed endless. There doesn't need to be 285 players, you can have an avg of 3.5 with much less players too...

Therefore I wonder, what kind of excersise this is you got there, as it seems worthy of high class university stochastic. In computer science we did a lot of stochastic, but never had an exercise as complex as this.
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