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August 3rd, 2011, 01:28 PM  #1 
Newbie Joined: Aug 2011 Posts: 1 Thanks: 0  probability:expectation problem
your friend will put 100 balls in a bag. Balls will be in 5 different colors and your friend will tell you how many balls for each color he put. you will draw a ball at random from the bag without looking at its color and will guess. If your estimate is correct the ball will be yours otherwise it will be your friend. This process will continue until you draw all the balls from the bag. The aim for both you and your friend is to win more balls. what can be the maximum number of balls that your friend will win from this game? 
August 4th, 2011, 02:43 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,821 Thanks: 723  Re: probability:expectation problem
Assuming you know the result after each draw, the maximum he can get is 99. In other words it is possible for you to guess wrong on every draw except the last one.

August 5th, 2011, 03:25 AM  #3 
Newbie Joined: Jul 2010 Posts: 4 Thanks: 0  Re: probability:expectation problem
What about if I tell him always the same color for all pick up?

August 5th, 2011, 06:02 AM  #4  
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: probability:expectation problem Quote:
 
August 5th, 2011, 01:01 PM  #5  
Global Moderator Joined: May 2007 Posts: 6,821 Thanks: 723  Re: probability:expectation problem Quote:
 
August 5th, 2011, 05:24 PM  #6 
Newbie Joined: Jul 2011 Posts: 16 Thanks: 0  Re: probability:expectation problem
Say there is 35 blue balls 25 red balls 40 green balls Wouldn't you generally win more by guessing green until they are all accounted for? So the maximum your friend can win against a logical player is 100  (the largest number of same coloured balls). If you're going to go for actual guessing then you aren't being a rational player and so your friend can win all 100. I suppose the other interpretation is that you should always guess the largest fraction of balls (so say if the first 6 are green, choose blue next). In that case you could are guaranteed only the last one. 
August 5th, 2011, 05:37 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: probability:expectation problem
What [color=#008000]mathman[/color] is saying is that it is possible (but not probable) for you to guess wrong every time until the last ball, at which point you know its color. Thus, the maximum your friend can get is 99. This is an unlikely scenario, but it is the maximum possible.

August 5th, 2011, 06:56 PM  #8 
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: probability:expectation problem
I think I'm thinking too generally. We're assuming a rational agent is playing the game, but I was thinking under the context of a random agent. So, perhaps my remark was not as accurate as I had thought. 

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