Question: In 37 of the 59 years from 1950 through 2008, the S&P 500 finished higher after the first 5 days of trading. In 32 of those 37 years, the S&P 500 finished higher for the 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 59 – year period:

S&P 500’s Annual Performance

First Week Higher Lower

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 5 days of trading, what is the probability that it finished higher for the year?

c. Are the two events “for-week performance” and “annual performance” independent? Explain.

d. Look up the performance after the first 5 days of 2009 and the 2009 annual performance of the S&P 500 at finance.yahoo.com. Comment on the results.