There are four dice in a drawer: one tetrahedron (4 sides), one hexahedron (i.e.,cube, 6-sides), and two octahedra (8 sides). Your friend secretly grabs one of the four dice at random. Let s be the number of sides on the chosen die.

Now your friend rolls the chosen die and without showing the die to you rolls it... Let R be the result of the roll.

(a) Use Bayes rule to find P(s = kIR = 3) for k = 4,6,8. Which die is most likely if R = 3?

(b) Which die is most likely if R = 6? Hint: You can either repeat the computation in (b), or you can reason based on your result in (b).

(c) Which die is most likely if R = 7? No computations are needed!