Easy prob question but I can't see it :(

• Aug 27th 2011, 06:43 AM
perla
Easy prob question but I can't see it :(
A hunter has 2 hunting dogs.

One day, on the trail of some animal, the hunter comes to a place where the road diverges into two paths. He knows that each dog, independent of the other, will choose the correct path with probability p. The hunter decides to let each dog choose a path, and if they agree, take that one, and if they disagree, to randomly pick a path. Is his strategy better than just letting one of the two dogs decide on a path?
• Aug 27th 2011, 08:50 AM
alexmahone
Re: Easy prob question but I can't see it :(
Quote:

Originally Posted by perla
A hunter has 2 hunting dogs.

One day, on the trail of some animal, the hunter comes to a place where the road diverges into two paths. He knows that each dog, independent of the other, will choose the correct path with probability p. The hunter decides to let each dog choose a path, and if they agree, take that one, and if they disagree, to randomly pick a path. Is his strategy better than just letting one of the two dogs decide on a path?

$\displaystyle Probability=p^2+2p(1-p)\times 0.5=p^2+p-p^2=p$

So, his strategy is exactly as good as just letting one of the two dogs decide on a path.
• Aug 27th 2011, 09:04 AM
MAX09
Re: Easy prob question but I can't see it :(
interesting question. though i'm unable to conclude a way to answer your question, i have a feeling that this could be more than probability. it appeared as though it was a decision making problem... have listed the possibilities in the image below....
• Aug 27th 2011, 10:01 PM
perla
Re: Easy prob question but I can't see it :(
Quote:

Originally Posted by alexmahone
$\displaystyle Probability=p^2+2p(1-p)\times 0.5=p^2+p-p^2=p$

So, his strategy is exactly as good as just letting one of the two dogs decide on a path.

Thank you for your reply. Why is there a 2 times p(1-p) and times 0.5?

Regards
• Aug 27th 2011, 11:06 PM
CaptainBlack
Re: Easy prob question but I can't see it :(
Quote:

Originally Posted by perla
Thank you for your reply. Why is there a 2 times p(1-p) and times 0.5?

Regards

Because there are two ways of the dogs disagreeing on the path dog1 could be right and 2 wrong or dog1 could be wrong and 2 right.

CB
• Aug 27th 2011, 11:10 PM
CaptainBlack
Re: Easy prob question but I can't see it :(
Quote:

Originally Posted by MAX09
interesting question. though i'm unable to conclude a way to answer your question, i have a feeling that this could be more than probability. it appeared as though it was a decision making problem... have listed the possibilities in the image below....

It is a pure probability problem, the decision rule is given the only question left is what is the probability of a correct outcome.

Your third possibility is redundant it is already present as leaf nodes on the first two branches.

CB
• Aug 28th 2011, 03:22 AM
MAX09
Re: Easy prob question but I can't see it :(
i thought the problem was to decide which of the two methods was better. now i see it..
the third offshoot from the centre was to analyse the second method by letting one of them pick a given way...
As alexmahone posted it, both methods turned out to have the same outcome.

A thought-provoking problem.