Problem 2. In a cup there is a mixture of 10 dice of different types: ...

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Problem 2. In a cup there is a mixture of 10 dice of different types: ...

Problem 2. In a cup there is a mixture of 10 dice of different types:

 1 four-sided die (i.e., four faces of 1, 2, 3, and 4)

 2 six-sided dice (i.e., the “regular” die)

 3 eight-sided dice (i.e., eight faces of 1, 2, ..., 8)

 4 twelve-sided dice (i.e., twelve faces of 1, 2, ..., 12)

All dice are fair (i.e., equal probability for all possible outcomes). I take one die from the cup at random, and, without showing to you, I roll it.

(1) If I tell you that the result is a 3, which die (4-, 6-, 8-, or 12-sided?) is the most probable?

(2) If I tell you that the result is a 6, which die is the most probable?

(3) If I tell you that the result is a 9, which die is the most probable? (hint: You may not need computations for this one..)

Find your answers to question (1) and (2) by calculating and comparing the probabilities of each of the four types of dice using Bayes’ theorem.

Show all work handwritten please

math Statistics-And-Probability

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