Your friend has asked for your help with a gambling problem. He is not sure that the casino is using fair dice. You know that a fair die has 6 numbers (1 to 6) all with equal probability of coming out at each toss.

You ask him to do an experiment: roll the die three times in sequence. After each roll, you will calculate a new probability that the die is rigged. Assume that each time you roll the die, it comes out 6.

Since we do not know the prior probability that the die is rigged, you will use a random probability as your "initial guess". Choose a number > 0 and < 1 as your starting probability that the die is rigged.

Now, use Bayes' theorem and calculate the probability that the die is rigged after getting the first 6.

The resulting probability will be your prior for the next roll and so on. Repeat three times. What is the probability (after observing three rolls of 6) that the die is rigged? Compare to the findings of your colleagues and compare the starting probabilities used. What do you observe?