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May 24th, 2017, 06:11 PM   #1
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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?
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May 24th, 2017, 06:20 PM   #2
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what is the payoff per bet?
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May 24th, 2017, 06:35 PM   #3
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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
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May 24th, 2017, 06:40 PM   #4
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Quote:
Originally Posted by romsek View Post
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
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May 24th, 2017, 07:08 PM   #5
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Quote:
Originally Posted by dthiaw View Post
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.
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May 25th, 2017, 10:03 AM   #6
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Hey Romsek, is there a way to write out concrete steps for this problem?
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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
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Ah so 45 dollars is the outcome that occurs the most, which is what makes it the answer?
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May 25th, 2017, 06:23 PM   #9
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$82.50
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