Question

Suppose that it snows in Greenland an average of once every 21 days, and when it does, glaciers have a 26% 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.)

Answer 1

Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(snows) = 1/21

P(does not snow) = 1 - 1/21 = 20/21

P(glacier growing | snows) = 0.26

P(glacier growing | does not snow) = 0.09

P(snows | glaciers are growing) = P(snows and glaciers are growing) / P(glaciers are growing)

= (1/21 x 0.26)/(1/21 x 0.26 + 20/21 x 0.09)

= 0.1262