About portfolio diversification and risk?

Suppose that you have $100,000 to invest for one year. You are considering buying stocks. There are many companies whose stock you could potentially buy. Suppose that each company you are considering is very risky: in one year, the company's stock will either be worth nothing, or worth four times its current value, with each outcome equally likely (that is, each outcome has a probability of ½). Assume for simplicity that there are no dividends and no inflation. Assume that each company’s fate is independent of each other company’s fate. Finally, assume for now that there are no brokerage cost or other transactions costs to buying stocks.

(a) Suppose you invest your entire $100,000 in one company's stock. What is the probability that you will wind up with nothing? What is the probability that you will wind up with $400,000? What is the expected (or average, or mean) value of your stock after one year?