3. The "random walk" theory of securities prices holds that price movements in disjoint time periods are independent of each other. Suppose that we record only whether the price is up or down each year and that the probability that our portfolio rises in price in any one year is 0.65. (This probability is approx- imately correct for a portfolio containing equal dollar amounts of all common stocks listed on the New York Stock Exchange.) (a) What is the probability that our portfolio goes up for three consecutive years? Give your answer to 3 decimal places. (b) If you know that the portfolio has risen in price two years in a row, cal- culate the probability that it will go down next year? Give your answer to 3 decimal places. (c) What is the probability that the portfolio's value moves in the same di- rection in both of the next two years? Give your answer to 3 decimal places.