Question

Suppose that it snows in Greenland an average of once every 27 days, and when it does, glaciers have a 23% chance of growing. When it does not snow in Greenland, glaciers have only a 7% 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

Answer: 0.1122

Explanation:

Let A denotes the event that it snows in Greenland.

Then A' denotes the event that it does not snow in Greenland.

Let G be the event that glaciers grows.

Given : Suppose that it snows in Greenland an average of once every 27 days.

i.e.
`P(A)=(1)/(27)`

Then,
`P(A')=1-P(A)=(26)/(27)`

Also, P(G|A)=0.23 and P(G|A')=0.07

By Bayes theorem , we have

`P(A|G)=(P(G|A)P(A))/(P(G|A)P(A)+P(G|A')P(A'))\\\\`

`=(0.23\cdot(1)/(27))/(0.23\cdot(1)/(27) + 0.07\cdot(26)/(27))\\\\=(0.0085185)/(0.0759259)\\\\=0.112195\approx0.1122`

Hence, the probability that it is snowing in Greenland when glaciers are growing= 0.1122