During the course of the 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 1/2, the fraction of mediocre items is 1/3, and the fraction of bad items is 1/6.

a) In a column, prepare the sample space for the experiment that consists of observing the day's production.

b) Assume a good item returns a profit of $2, a mediocre item a profit of $1, and a bad item yields nothing. Let X be the random variable describing the total profit.