At the beginning of each year, an investment newsletter predicts whether or not the stock market will rise over the following year. Historical evidence reveals that there is a 60% chance of the market rising, in any given year. The newsletter has predicted a rise for 70% of the years when the market actually rose, and has predicted a rise for 30% of the years when the market actually fell. Find the probability that the newsletter's prediction for next year will be correct.
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