Problem 4. During the course of a day a machine turns out two items, one in the morning and one

in the afternoon. The quality of each item is measured as good (G), mediocre (M), or

bad (B). The long-run fraction of good items the machine produces is 0.3, the fraction of

mediocre items is 0.4, and the fraction of bad items is 0.3.

Assume a good item returns a profit of $4, a mediocre item a profit of $1, and a bad

item yields nothing. Assuming that the qualities of the morning and afternoon items are

independent, derive the probability distribution of the total profit for the day.