exercise:F626b53b6b: Difference between revisions
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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> Smith is in jail and has 3 dollars; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets <math>A</math> dollars, he wins <math>A</math> dollars with probability .4 and loses <math>A</math> d...") |
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\newcommand{\mathds}{\mathbb}</math></div> Smith is in jail and has 3 dollars; he can get out on | \newcommand{\mathds}{\mathbb}</math></div> Smith is in jail and has 3 dollars; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets <math>A</math> dollars, he wins <math>A</math> dollars with probability .4 and loses <math>A</math> dollars with probability .6. Find the probability that he wins 8 dollars before losing all of his money if | ||
bail if he has 8 dollars. A guard agrees to make a series of bets with him. | <ul style="list-style-type:lower-alpha"><li> he bets 1 dollar each time (timid strategy). | ||
If | |||
Smith bets <math>A</math> dollars, he wins <math>A</math> dollars with probability .4 and loses | |||
<math>A</math> dollars with probability .6. Find the probability that he wins 8 dollars | |||
before losing all of his money if | |||
<ul><li> he bets 1 dollar each time (timid strategy). | |||
</li> | </li> | ||
<li> he bets, each time, as much as possible but not more than necessary to | <li> he bets, each time, as much as possible but not more than necessary to | ||
Latest revision as of 22:26, 15 June 2024
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Smith is in jail and has 3 dollars; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets [math]A[/math] dollars, he wins [math]A[/math] dollars with probability .4 and loses [math]A[/math] dollars with probability .6. Find the probability that he wins 8 dollars before losing all of his money if
- he bets 1 dollar each time (timid strategy).
- he bets, each time, as much as possible but not more than necessary to bring his fortune up to 8 dollars (bold strategy).
- Which strategy gives Smith the better chance of getting out of jail?