exercise:A9bea67f5b: 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> (from Sholander<ref group="Notes" >M. Sholander, Problem \#1034, ''Mathematics Magazine,'' vol. 52, no.\ 3 (May 1979), p. 183.</ref>) In a standard clover-leaf interchange, there are four ramps for making right-hand turns, and inside these four ra...") |
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(from Sholander<ref group="Notes" >M. Sholander, Problem #1034, ''Mathematics Magazine,'' vol. 52, | |||
no. 3 (May 1979), p. 183.</ref>) In a standard | |||
(from Sholander<ref group="Notes" >M. Sholander, Problem | |||
no. | |||
clover-leaf interchange, there are four ramps for making right-hand turns, and inside these | clover-leaf interchange, there are four ramps for making right-hand turns, and inside these | ||
four ramps, there are four more ramps for making left-hand turns. Your car approaches the | four ramps, there are four more ramps for making left-hand turns. Your car approaches the | ||
interchange from the south. A mechanism has been installed so that at each point where there | interchange from the south. A mechanism has been installed so that at each point where there | ||
exists a choice of directions, the car turns to the right with fixed probability <math>r</math>. | exists a choice of directions, the car turns to the right with fixed probability <math>r</math>. | ||
<ul><li> | <ul style="list-style-type:lower-alpha"><li> | ||
If <math>r = 1/2</math>, what is your chance of emerging from the interchange going west? | If <math>r = 1/2</math>, what is your chance of emerging from the interchange going west? | ||
</li> | </li> | ||
Latest revision as of 21:15, 12 June 2024
(from Sholander[Notes 1]) In a standard clover-leaf interchange, there are four ramps for making right-hand turns, and inside these four ramps, there are four more ramps for making left-hand turns. Your car approaches the interchange from the south. A mechanism has been installed so that at each point where there exists a choice of directions, the car turns to the right with fixed probability [math]r[/math].
- If [math]r = 1/2[/math], what is your chance of emerging from the interchange going west?
- Find the value of [math]r[/math] that maximizes your chance of a westward departure from the interchange.
Notes