exercise:A9bea67f5b: Difference between revisions
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(from Sholander<ref group="Notes" >M. Sholander, Problem \#1034, ''Mathematics Magazine,'' vol. 52, | (from Sholander<ref group="Notes" >M. Sholander, Problem \#1034, ''Mathematics Magazine,'' vol. 52, | ||
no. | 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 | 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 | ||
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