Task 2. Let's consider the "same" experiment and scoring scheme in Task 1 except that now the die is "weighted" so that the probability of getting the various rolls of the die is as follows:

Roll 1 2 3 4 5 6
Probability 1/4 1/6 1/6 1/6 1/6 1/12

Find the expected value (don't forget the coin toss). In order to make a little profit in the "long run", what should your minimum charge be for the privilege of playing this game?