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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1 Answer

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.

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What if he is? How does it make a difference? –  shelagh Dec 10 '12 at 18:52
The point is that Monty knows where the car is and chooses a door to open based on the door originally chosen by the contestant. In this case the town location is chosen and the information is independent of where the driver planned to go. –  Ross Millikan Dec 10 '12 at 18:58
Does intentional vs coincidental revealing of the third door makes a difference? I thought MHP is just a shift of choices of probabilities from (1/3) vs ( 2/3 )? –  shelagh Dec 10 '12 at 19:14
@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
The shift occurs because Monty knows about your choice, and he cannot open the door you originally chose. The cyclist has no such restriction. –  Ben Millwood Dec 10 '12 at 19:18