Suppose that it snows in Greenland an average of once every

Suppose that it snows in Greenland an average of once every 21 days, and when it does, glaciers have a 24% chance of growing. When it does not snow in Greenland, glaciers have only a 9% chance of growing. What is the probability that it is snowing in Greenland when glaciers are growing? (Round your answer to four decimal places.

Solution

There is a 95% chance it is not snowing in Greenland, and a 5% chance of a glacier growing, for a total probability of (0.95)(0.05) = 0.0475 = 4.75%. There is a 5% chance it is snowing in Greenland, and a 15% chance of a glacier growing, for a total probability of (0.05)(0.15) = 0.0075 = 0.75%. Therefore, the probability that it is snowing when glaciers are growing is (0.75%)/(0.75% + 4.75%) = 13.6%