People use animals to predict outcomes of sporting events and elections mostly by having the animals pick between two containers of food, each representing one of the two teams or the two candidates involved. Probably the most famous of these is Paul the Octopus from Germany who was correct in all eight of his predictions for the 2010 World Cup (Nov 2022 article). Do Paul's results provide strong evidence that he was doing something other than randomly guessing and perhaps had some psychic power? Let p (or if you are looking at the one proportion inference app) represent Paul's probability of picking the winning team. Provide a one-sentence interpretation of this probability, using the symbol to represent the unknown value.

Can we use a "coin tossing" simulation to represent the scenario where Paul is simply guessing? Explain (and discuss any limitations you see in using this model to represent Paul's behavior).

If we let p represent Paul's probability of picking the winning team, what is the value of p if Paul was randomly guessing? If Paul had some psychic power, what does this imply about the value of p?