exercise:09249c985d: 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> Recall that in the World Series the first team to win four games wins the series. The series can go at most seven games. Assume that the Red Sox and the Mets are playing the series. Assume that the Mets win each game with probability <math>p</m...") |
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Recall that in the World Series the first team to win four games wins the series. The series can go at most seven games. Assume that the Red | |||
games wins the series. The series can go at most seven games. Assume that the Red | |||
Sox and the Mets are playing the series. Assume that the Mets win each game with | Sox and the Mets are playing the series. Assume that the Mets win each game with | ||
probability <math>p</math>. Fermat observed that even though the series might not go seven | probability <math>p</math>. Fermat observed that even though the series might not go seven | ||
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that they win four or more game in a series that was forced to go seven games no | that they win four or more game in a series that was forced to go seven games no | ||
matter who wins the individual games. | matter who wins the individual games. | ||
<ul><li> Using the program ''' PowerCurve''' of [[guide:E54e650503#exam 3.12 |Example]] find the probability | <ul style="list-style-type:lower-alpha"><li> Using the program ''' PowerCurve''' of [[guide:E54e650503#exam 3.12 |Example]] find the probability | ||
that the Mets win the series for the cases <math>p = .5</math>, <math>p = .6</math>, <math>p =.7</math>. | that the Mets win the series for the cases <math>p = .5</math>, <math>p = .6</math>, <math>p =.7</math>. | ||
</li> | </li> | ||
Latest revision as of 23:07, 12 June 2024
Recall that in the World Series the first team to win four games wins the series. The series can go at most seven games. Assume that the Red Sox and the Mets are playing the series. Assume that the Mets win each game with probability [math]p[/math]. Fermat observed that even though the series might not go seven games, the probability that the Mets win the series is the same as the probability that they win four or more game in a series that was forced to go seven games no matter who wins the individual games.
- Using the program PowerCurve of Example find the probability that the Mets win the series for the cases [math]p = .5[/math], [math]p = .6[/math], [math]p =.7[/math].
- Assume that the Mets have probability .6 of winning each game. Use the program PowerCurve to find a value of [math]n[/math] so that, if the series goes to the first team to win more than half the games, the Mets will have a 95 percent chance of winning the series. Choose [math]n[/math] as small as possible.