Question

Assume you have two dices: one has 6 faces with letters from A to B (i.e., A, …, F) and the other has 20 faces with numbers from 1 to 20 (i.e., 1, …, 20)? We assume that the number dice is even, meaning that the number dice gives a number from 1 to 20 with the probability 1/20 of each. However, the letter dice is not even. The letter dice always gives you a letter from A to F with the following probabilities: Prob(A)=1/4, Prob(B)=1/4, Prob(C)=1/6, Prob(D)=1/6, Prob(E)=1/12, Prob(F)=1/12. Questions: what is the entropy when a gambler rolls the two dices together? Please include necessary steps before you determine the numerical result.

Answer 1