My Math Forum Finding an expected value

 May 24th, 2017, 06:11 PM #1 Member   Joined: Apr 2017 From: PA Posts: 34 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, 06:20 PM #2 Member   Joined: Jan 2017 From: California Posts: 65 Thanks: 5 what is the payoff per bet?
 May 24th, 2017, 06:35 PM #3 Senior Member     Joined: Sep 2015 From: CA Posts: 1,264 Thanks: 650 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, 06:40 PM   #4
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Quote:
 Originally Posted by romsek 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
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, 07:08 PM   #5
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Quote:
 Originally Posted by dthiaw Hi Romsek am i missing something or what? it was neverr stated how much the player was going to win for betting
I just assumed they win whatever they wager.

If you have 80, and win with a bet of 40 you end up with 120. If you lose you end up with 40.

 May 25th, 2017, 10:03 AM #6 Member   Joined: Apr 2017 From: PA Posts: 34 Thanks: 0 Hey Romsek, is there a way to write out concrete steps for this problem?
May 25th, 2017, 01:52 PM   #7
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This seems pretty intuitive to me. try it
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 May 25th, 2017, 06:13 PM #8 Member   Joined: Apr 2017 From: PA Posts: 34 Thanks: 0 Ah so 45 dollars is the outcome that occurs the most, which is what makes it the answer?
 May 25th, 2017, 06:23 PM #9 Member   Joined: Jan 2017 From: California Posts: 65 Thanks: 5 \$82.50 Thanks from poopeyey2

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