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September 15th, 2008, 07:15 AM  #1 
Newbie Joined: Sep 2008 Posts: 7 Thanks: 0  Probabilities of getting a golden coin??
Imagine that in a small town in Ireland , there is a rich old person who for the last 5 years has been throwing thousands of golden coins from his window. He starts throwing coins almost everyday at 00:00 till 01.50 a.m ( 12.76 % ) , or between 01.51 till 03.00 a.m (14.44 % ) Also between 03.01 till 04.45 a.m (16.99 %) As the dawn approaches he also throws between 04.45 till 06.00 a.m (13.97 %) or between 06.01 till 07.50 (16.91%) But he throws the most between 07.51 till 09.00 a.m (22.09%) About 8 % of the days he doesn’t throw any coins at all. The rich old person throws between 1 and 8 coins everyday but at different times. My question is : If I go to Ireland and wait under his window at 07:52 a.m and wait there till 09.00 a.m ¿¿how are my chances of getting a coin?? Also, If the rich old person has already thrown some coins during the night , it decreases my possibilities of me getting one golden coin ???? Also one final question: If I wait under his window for 1000 days . Will I get the 22.09 % of his coins or more??? Thanks for your help. 
September 15th, 2008, 09:16 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Probabilities of getting a golden coin??
The problem isn't wellspecified. Does he choose one interval to throw all the coins on, or only one? How does he choose how many to throw  uniformly at random from 1 to 8? And why don't the probabilities add up? Get any help elsewhere yet? 
September 15th, 2008, 10:42 AM  #3 
Newbie Joined: Sep 2008 Posts: 7 Thanks: 0  Re: Probabilities of getting a golden coin??
[quote="CRGreathouse"]The problem isn't wellspecified. Does he choose one interval to throw all the coins on, or only one? How does he choose how many to throw  uniformly at random from 1 to 8? And why don't the probabilities add up? You are right, the problem isn't well specified. Let's imagine that he has thrown 5000 coins in the last five years and someone has counted the coins as they were thrown. So we have the following percentage: aprox: 00:00 till 01.50 a.m :12.76 % (638 thrown coins ) 01.51 till 03.00 a.m :14.44 % (722 thrown coins ) 03.01 till 04.45 a.m (16.99 %) ( 849 thrown coins) 04.45 till 06.00 a.m :13.97 % ( 698 thrown coins ) 06.01 till 07.50 a.m :16.91% (845 thrown coins ) 07.51 till 09.00 a.m :22.09% (1104 thrown coins ) 1He throws the coins one at a time , totally at random 2On a given day , he can throw between 0 and 8 coins. Thanks for your help. 
September 15th, 2008, 11:15 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Probabilities of getting a golden coin??
So the probabilities given add up to 97.16% (if I haven't added wrong), and the problem says no coin is thrown 8% of the time. Is no coin thrown (100%  97.15%) + 8% of the time, or should the probabilities add to 92%, or should the probabilities add to 100% (and 8% of the time, the result is ignored)?

September 15th, 2008, 10:45 PM  #5  
Newbie Joined: Sep 2008 Posts: 7 Thanks: 0  Re: Probabilities of getting a golden coin?? Quote:
The possibilies of the thrown coins should have added up to 100 % . So in this case I imagine should be 100%  8%. Please keep in mind that i'm not particular good at maths and i'm from Spain so my description of the problem become more difficult. Thanks very much. Sergio  

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