You are involved in a risky business venture where three outcomes are possible:
(1) You will lose not only your initial investment ($5000) but an additional $3000;
(2) You will just make back your initial investment (for a net gain of $0); or
(3) You will make back your initial investment plus an extra $10,000. The probability of (1) is half as large as the probability of (2), and the probability of (3) is one-third as large as the probability of (2).
a. Find the individual probabilities of (1), (2), and (3). (They should sum to 1.)
b. Find the expected value and standard deviation of your net gain (or loss) from this venture.