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Lab Rat on the Run

Consider a lab rat in a maze. There are four paths that can be taken with equal probability. Path A leads to exit in 5 minutes. Path B leads back to start and takes 8 minutes. Path C leads to exit in 3 minutes and last path D is 2 minutes long and leads back to start. What is the expected escape time of this poor rat from the maze?

t = (1/4)*5 +  (1/4)*(8+t) +  (1/4)*3  + (1/4)*(2+t)
t = 9


Víctor Ortiga

As I see it 7 minutes and 20 sec. These are the posible combinations with the time required and each posibility (suposing the rat will never choose the same path twice):

3' C 25.000% 5' A 25.000% 5' DC 8.333% (25%33,33%) 7' DA 8.333% 11' BC 8.333% 13' BA 8.333% 13' BDC 4.167% (25%33,33%*50%) 13' DBC 4.167% 15' BDA 4.167% 15' DBA 4.167%

so 30.25+50.25+...+15*0.04167=7.33

I don't know why but it does not match with the solution given, so I would love anyone claryfing it to me.


Víctor Ortiga

I messed it up with the spaces. 3' C 25.000% 5' A 25.000% 5' DC 8.333% (25%33,33%) 7' DA 8.333% 11' BC 8.333% 13' BA 8.333% 13' BDC 4.167% (25%33,33%*50%) 13' DBC 4.167% 15' BDA 4.167% 15' DBA 4.167%

Víctor Ortiga

3' C 25.000%

5' A 25.000%

5' DC 8.333% (25%33,33%)

7' DA 8.333%

11' BC 8.333%

13' BA 8.333%

13' BDC 4.167% (25%33,33%*50%)

13' DBC 4.167%

15' BDA 4.167%

15' DBA 4.167%

We should have a edit/delete option; or at least a preview xD

Jot Sarup
 t = (1/4)*5 +  (1/4)*(16+t) +  (1/4)*3  + (1/4)*(4+t)

Should the Solution be this as t is the time to exit from a particular point (not the start). So to reach the start, it will take twice the time in case B and D

background tom

I cant see why this is the answer, there is one combination of routes that yeilds this answer, with a probability of 0.015625 that it will be taken. However if you said that the answer was 5 minutes there are two different routes that could be taken given a probability of 0.3125 that this time is achieved. This is the most likely time and therefore the expected time...


Can you elaborate on your solution? I'm not sure I understand your spoiler(8+t) and (2+t) factors since t is expected time inclusive of any failed attempts.


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Submitted by
Yiğit Oktar
over 4 years ago
Difficulty 6.0 ?

probability expected value