Question: Extra Credit II - Bayesian Analysis (110.0 points)
An airline is trying to determine whether the price of fuel will rise or fall in the near future in order to determine whether to negotiate a fuel contract now or later. The airline executives believe there is an 65% chance that the cost of fuel will fall. However, they are risk-averse and would prefer to hire an analyst to obtain more information. The airline executives 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 executives hired the analyst, and the analyst issued a report predicting that the cost of fuel would fall. What is the probability that the price of fuel will fall given the analyst prediction of such a decrease? You should carry your calculations to 4 decimal places and round of your answer to 2.

1. .65
2. .68
3. .74
4. .87

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