So a friend asked me that:
A cop is going after a criminal with 2 police dogs. At some point the road diverges. The cop knows that the probability that a dog will go in the right way after the criminal is $p$ independently with other dogs choice.
The cop decides as follows: If both dogs have chosen the same way, he will go that way. If each dog has chosen a differnet path, he will choose the path to go through, randomally.
Now the question is: Is this method is better then letting one of the dogs choose the path?
It feels like I can use Bernoulli distribution to build the equation I need but I can't figure out how.