Question: 27 In 35 of the 56 years from 1950 through 2005, the S&P 500 finished higher after the first 5 days of trading. In 30 of those 35 years, the S&P 500 finished higher for a year. Is a good first week a good omen for the upcoming year? The following table gives the first-week and annual performance over this 56-year period

a. If a year is selected at random, what is the probability that the S&P 500 finished higher for the year?

b. Given that the S&P 500 finished higher after the first five days of trading, what is the probability that it finished higher for the year?

c. Are the two events "first week performance" and "annual performance" statistically independent? Explain.

d. Look up the performance after the first five days of 2006 and the 2006 annual performance of the S&P 500 at finance.yahoo.com. Comment on the results