"Since 1950, the January Barometer has predicted the annual course of the stock market with amazing accuracy" (1998 Stock Trader's Almanac). Over the 48 years from 1950 through 1997, the stock market has been up in January 31 times; it has been up for the year 36 times; and it has been up for the year and up for January 29 times.

Find the chance the stock market will be up in January.

(b)Find the chance the stock market will be up for the year.

(c)What is the chance the stock market will be up for the year given it is up in January?

(d)Do the chances suggest that the stock market's "January performance" and its "annual performance" are independent events? Explain with calculation.