At the Beginning of Each Year, an Investment Newsletter Predicts

Short Answer

At the beginning of each year, an investment newsletter predicts whether or not the stock market will rise over the coming year. Historical evidence reveals that there is a 75% chance that the stock market will rise in any given year. The newsletter has predicted a rise for 80% of the years when the market actually rose, and has predicted a rise for 40% of the years when the market fell. Find the probability that the newsletter's prediction for next year will be correct.