When creating a probability distribution, we can estimate the probabilities empirically using a simulation.

At a college baseball stadium, every game features a race between three mascots: one dressed as a peanut, one dressed as a hot dog, and one dressed as a cup of soda. The winner of the race determines what discount will be available at the concession stand for the rest of the game: [latex]$1[/latex] bags of peanuts, [latex]$1[/latex] hot dogs, or [latex]$1[/latex] soft drinks. For now, let’s assume that all three mascots are equally likely to win the race, and each race is independent.

Since we’re assuming all three mascots are equally likely to win in each race, let’s say that our statistics class decides to carry out the simulation by rolling dice: 1 and 2 represent Peanut, 3 and 4 represent Hot Dog, and 5 and 6 represent Soda. How many times would you expect to get discounted peanuts if you attended 10 games?