Imagine 100 book bags, each of which contains 1,000 poker chips. Forty-five bags contain 700 black chips and 300 red chips. The other 55 bags contain 300 black chips and 700 red chips. You cannot see inside any of the bags. One of the bags is selected at random by means of a coin toss.
Consider the following three questions about the book bag.
a. What probability would you assign to the event that the selected bag contains predominantly black chips?
b. Now imagine that 12 chips are drawn, with replacement, from the selected bag.
These 12 draws produce 8 blacks and 4 reds. Would you use the new information about the drawing of chips to revise your probability that the selected bag contains predominantly black chips? If so, what new probability would you assign?
c. In addition to giving your best probability estimate in question b, consider a range: a low estimate and a high estimate so that you feel 90 percent confident that the right answer will lie between your low estimate and your high estimate. Try not to make the range between your low estimate and high estimate too narrow. Otherwise, you will appear overconfident. At the same time, try not to make the range between your low estimate and high estimate too wide. This will make you appear underconfident. If you are well-calibrated, you should expect the true probability to lie outside the range between your low estimate and your high estimate one time in ten.