# Monty Hall Application

Driver A comes to a 3 way path junction but is not sure which one to take. Just as he decides to take path 1, a cyclist came by and told driver A all he knows is that he is going on path 3 which would bring him to town. Driver A is not heading to town but the seaside. Should he change to path 2?

Driver B encounters the cyclist before he can decide which path to take to the village. Is his chance less than driver A because he cannot switch?

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If we presume that the seaside and town are different directions, each driver has $\frac 12$ chance going on path $1$ or $2$ and $0$ chance going on path $3$. This is not a Monty Hall situation because the cyclist is not reacting to the driver's choice.
@shelagh: I don't understand your question. Initially the driver thinks the town has $\frac 13$ chance to be in any of the directions. After the new information, he thinks it is $\frac 12$ for each of two locations, which are completely equivalent in this case. – Ross Millikan Dec 10 '12 at 19:18