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May 24th, 2017, 07:11 PM  #1 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0  Finding an expected value
You have 80 dollars and play the following game. An urn contains two white balls and two black balls. You draw the balls out one at a time without replacement until all the balls are gone. On each draw, you bet half of your present fortune that you will draw a white ball. What is your expected final fortune? For this one, I thought about summing up 40 (1/2) 40 (1/2) to get 0, then I knew if I took one of the urns out, there could be a 1/3 or 2/3 chance of getting a white ball, so, I added 40(1/3)40 (1/3) to get 0. Also, I did the same procedure again with the 2/3. But all I kept getting was zero. How do u find the correct expected value? 
May 24th, 2017, 07:20 PM  #2 
Member Joined: Jan 2017 From: California Posts: 80 Thanks: 8 
what is the payoff per bet?

May 24th, 2017, 07:35 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 1,692 Thanks: 860 
I'm seeing that every possible sequence of draws results in a final cash value of \$45 The problem is symmetric in black and white so all draw sequences are equally likely. So the expected value is clearly \$45 
May 24th, 2017, 07:40 PM  #4 
Member Joined: Jan 2017 From: California Posts: 80 Thanks: 8  Hi Romsek am i missing something or what? it was neverr stated how much the player was going to win for betting

May 24th, 2017, 08:08 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 1,692 Thanks: 860  
May 25th, 2017, 11:03 AM  #6 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0 
Hey Romsek, is there a way to write out concrete steps for this problem?

May 25th, 2017, 02:52 PM  #7 
Member Joined: Jan 2017 From: California Posts: 80 Thanks: 8 
This seems pretty intuitive to me. try it

May 25th, 2017, 07:13 PM  #8 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0 
Ah so 45 dollars is the outcome that occurs the most, which is what makes it the answer?

May 25th, 2017, 07:23 PM  #9 
Member Joined: Jan 2017 From: California Posts: 80 Thanks: 8 
$82.50


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