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August 3rd, 2011, 01:28 PM   #1
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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?
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August 4th, 2011, 02:43 PM   #2
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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.
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August 5th, 2011, 03:25 AM   #3
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Re: probability:expectation problem

What about if I tell him always the same color for all pick up?
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August 5th, 2011, 06:02 AM   #4
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Re: probability:expectation problem

Quote:
Originally Posted by mathman
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.
Why is the last one excluded? I was thinking it'd be possible for him to get every ball.
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August 5th, 2011, 01:01 PM   #5
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Re: probability:expectation problem

Quote:
Originally Posted by CherryPi
Quote:
Originally Posted by mathman
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.
Why is the last one excluded? I was thinking it'd be possible for him to get every ball.
I assumed that after each ball is chosen you are told (after you guess) what is the correct answer. When there is only one ball left you should know the color - guess not needed.
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August 5th, 2011, 05:24 PM   #6
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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.
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August 5th, 2011, 05:37 PM   #7
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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.
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August 5th, 2011, 06:56 PM   #8
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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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