1. ) In 38 of the 61 years from 1950 to 2010, the S&P (Standard and Poor's 500 Index) finished higher after the first five days of trading. In 33 of those 38 years the S&P 500 finished higher for the year. An investor wishes to get an idea whether a good first week is a good omen for the upcoming year. The relationship between the first-week and annual performance over tis 61-year period is given by the following table

	S&P 500's annual performance
First week	Higher	Lower
Higher	33	5
Lower	12	11

1. If a year isselected at random, what is the probability that the S&P finished higher for the year?
2. Given that the S&P finished higher after the first five days of trading, what is the probability that it finished higher for the year?
3. Are the two events, first-week performance and annual performance, statistically independent? Explain.