A hunter has two dogs. Once, when he was lost in the woods, he went to the fork in the road. The hunter knows that each of the dogs with probability \(p\) will choose the way home. He decided to release the dogs in turn. If both choose the same road, he will follow them; if they are separated, the hunter will choose the road, by throwing a coin. Will this increase the hunter’s chances of choosing the way home, compared to if he had only one dog?