Question

Suppose an urn contains 2 white balls and 3 blue balls (balls are identical). Consider the following game:

Step 1: You roll a fair 6-sided die on which

One side is labelled '0'

Two sides are labelled '1', and

Three sides are labelled '2'.

Step 2: If the outcome of the roll is k (where k=0, 1 or 2), then you select a subset of k balls from the urn in such a way that all subsets of k balls are equally likely to be chosen. Note: Balls are selected without replacement (If k=0, then no ball is selected from the urn),

Step 3: For every white ball that you select, you receive $2, but for every blue ball that you select, you must pay $1.

Let X denote how much you win or lose playing this game.

(a.)State ImX, the Image of X

(b.)Determine P_X(x), the probability mass function for X. Give reasons for your calculations.

(c.)Compute E(X), the expected value of X.