In 42 of the 64 years from 1950 through 2014,the S& P 500 finished higher after the first five days of trading (in 2011 there was virtually no change). In 37 out of 42 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 64-year period. S&P 500's Annual Performance
First week Higher Lower Total
Higher 37 5 42
Lower 11 11 22
Total 48 16 64

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

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

c) Are the two events "first week performance" and "annual performance"
independent or dependent? Explain why.