An airline is trying to determine whether the price of fuel will rise or fall in the future. They believe there is a 65% chance that the cost of fuel will fall. However, they are risk-averse and prefer to hire an analyst. The airline execs have found that when the price of fuel fell, the analyst correctly predicted the decrease in cost 90% of the time. When the price of fuel rose, the analyst correctly predicted the increase 75% of the time. The execs hired the analyst and he issued a report predicting that the cost of fuel would fall. What is the probability the price of fuel will fall given this prediction. Round to the answer to 2 decimal places.
This solution provides calculations for probability.