Suppose that it snows in Greenland an average of once every

Suppose that it snows in Greenland an average of once every 29 days, and when it does, glaciers have a 26% chance of growing. When it does not snow in Greenland, glaciers have only a 3% 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

Let us denote the event that it is snowing with S, and not snowing with ~S. Also, the event that the glaciers are growing is G, and not growing is ~G.

We are given that:

P(G|S) = 0.26 (the probability that the glaciers are growing given that it is snowing)

P(G|~S) = 0.03 (the probability that the glaciers are growing given that it is not snowing).

And we want to find:

P(S|G) = ? (the probability that it is snowing given that the glaciers are growing).

By Bayes\' thm:

P(S|G) = [ P(G|S) * P(S) ] / [ P(G) ]

P(S) is given - we know that it snows every 29 days. Therefore:

P(S) = 1/29 for any given day, and

P(~S) = 28/29.

So we use the law of total probability to find P(G):

P(G) = P(G|S)*P(S) + P(G|~S)*P(~S)

= 0.26 * 1/29 + 0.03 * 28/29

= 0.0379