you are playing a game of hide - and - seek with two friends . while one of your friends counts , you and your other friend are given a chance to hide in one of five possible hiding spots . you are each allowed to pick a hiding spot , and are permitted to share a hiding spot . your friend finishes counting and checks one of the five hiding spots . assuming that everyone's decisions are made uniformly at random , what are the chances that your friend does not find anyone in the first spot that they check ?