If any color gives them a better chance to get on the ride, they'll all pick that color. Outcome What you guess ⚃. What can we say about this? You have the guarantee your boss asked for: No matter what color die the guest chooses, the set you guess will include the true color 70% of the time. Still don't believe me? Say you're OK with subjective probabilities and say that guests choose dice randomly so that the prior probabilities of colors are the same. Now suppose the guest rolls ⚃. Would you be tempted to say that there is a 70% chance the true color was white? In this situation, the posterior probability of each color is proportional to the chance that color rolls ⚃. Look at the right column of the big probability table. "We have a procedure that maps dice rolls to sets of colors. We've designed the procedure so that, if we roll any of the dice millions of times and compute the corresponding sets of colors, at least 70% of those sets will contain the true color. For the dice roll we observed in this particular instance our procedure maps the outcome to." Guest True color Outcome Guess Amy red Bob yellow Carlos green Zander white ⚃. All we can guarantee is that, in the long run, 70% of the guesses will contain the true colors. Even if you have a prior distribution over the colors and calculate the probabilities, they might be much larger or smaller than 70%. When talking about confidence, we give no guarantee-none!-about what the actual true color is in any particular instance.