Assume that each monkey has a strong preference between red, green, and blue M&M’s. Further, assume that the possible orderings of the preferences are equally distributed in the population. That is to say that each of the 6 possible orderings ( R>G>B or R>B>G or B>R>G or B>G>R or G>B>R or G>R>B) are found with equal frequency in the population. Lastly assume that when presented with two M&Ms of different colors they always eat the M&M with the color they prefer.
In an experiment, a random monkey is chosen from the population and presented with a Red and a Green M&M. In the first round, the monkey eats the one based on their personal preference between the colors. The remaining M&M is left on the table and a Blue M&M is added so that there are again two M&M’s on the table. In the second round, the monkey again chooses to eat one of the M&M’s based on their color preference.
- What is the chance that the red M&M is not eaten in the first round?
- What is the chance that the green M&M is not eaten in the first round?
- What is the chance that the Blue M&M is not eaten in the second round?
[Mattingly 2022]
