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roulette

 
 
Reply Fri 20 Jan, 2006 05:01 pm
Roulette:
- 37 numbers (0, 1, 2,... 36).
- 150 times the roulette wheel is turned


Participants:
- There are 37 participants.
- Every paticipant chooses one number out (0, 1, 2,... 36).
- Every participant only plays on the 1st, 6th, 11th, 16th, 21st, 26th, 31st, 36th, 41st, 46th, 51st, 56th, 61st, 66th, 71st, 76th, 81st, 86th, 91st, 96th, 101st, 106th, 111st, 116th, 121st, 126th, 131st, 136th, 141st and 146th roulette turns. So only on 30 turns - every 5th turn, starting with the 1st and always with the same initial choosen number.


Question: How many of these 37 participants did not win once, after 150
roulette turns? And how do you calculate this?


Whim
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markr
 
  1  
Reply Fri 20 Jan, 2006 10:50 pm
The every 5th turn requirement just means that there are 30 turns.

Assuming everyone has to pick a different number; so that all numbers (0-36) are bet each turn, at least seven players did not win at all. Since there are only 30 turns, there can be at most 30 winners. If the same number comes up every time, there will be only one winner. Therefore the number of winners (at least one win) is greater than zero and less than 31.

Are you looking for the mean number of winners?
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whimsical
 
  1  
Reply Sat 21 Jan, 2006 03:44 am
I found this problem, and I guess the mean number of winners, will answer the question too. So yes please.
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markr
 
  1  
Reply Sat 21 Jan, 2006 12:51 pm
I think the mean number of non-winners might be:
37 * (36/37)^30
which is approximately 16.26.
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