In 41 of the 63 years from 1950 through 2013 (in 2011 there was virtually no change), the S& P 500 finished higher after the first five days of trading. In 36 out of 41 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 63- 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 €œfirst- week performance€ and €œannual performance€ independent? Explain.
d. Look up the performance after the first five days of 2014 and the 2014 annual performance of the S& P 500 at finance. yahoo.com. Comment on the results.

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S&P 500'S ANNUAL PERFORMANCE FIRST WEEK Higher Lower Higher Lower 36