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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> 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...")
 
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<div class="d-none"><math>
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
\newcommand{\NA}{{\rm NA}}
\newcommand{\mat}[1]{{\bf#1}}
\newcommand{\exref}[1]{\ref{##1}}
\newcommand{\secstoprocess}{\all}
\newcommand{\NA}{{\rm NA}}
\newcommand{\mathds}{\mathbb}</math></div> 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
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?
present fortune that you will draw a white ball.  What is your expected final fortune?

Latest revision as of 16:31, 14 June 2024

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?