Question

Galadriel has two six-sided dice, one with the standard faces numbered through 6 and one with three faces numbered 3 and three numbered 6. Assume the dice are fair in the sense that on a single roll of either die, each of the six physical faces is equally likely to come up. Galadriel selects one of the dice at random, with probability p ∈ (0,1) that she selects the standard die. Assume that all subsequent rolls of the selected die are mutually independent. She rolls the die once and 3 comes up. What is the probability that the die is the standard one? She rolls the die again and this time 6 comes up. Now what is the probability that the die is the standard one? She rolls the die a third time and a 5 comes up. Now what is the probability that the die is the standard one?

          Galadriel has two six-sided dice, one with the standard faces numbered through 6 and one with three faces numbered 3 and three numbered 6. Assume the dice are fair in the sense that on a single roll of either die, each of the six physical faces is equally likely to come up. Galadriel selects one of the dice at random, with probability p ∈ (0,1) that she selects the standard die. Assume that all subsequent rolls of the selected die are mutually independent. She rolls the die once and 3 comes up. What is the probability that the die is the standard one? She rolls the die again and this time 6 comes up. Now what is the probability that the die is the standard one? She rolls the die a third time and a 5 comes up. Now what is the probability that the die is the standard one?

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