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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.)

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JeanaShupp

Answer: 0.1122

Step-by-step 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. [tex]P(A)=\dfrac{1}{27}[/tex]      

Then,  [tex]P(A')=1-P(A)=\dfrac{26}{27}[/tex]      

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

By Bayes theorem , we have

[tex]P(A|G)=\dfrac{P(G|A)P(A)}{P(G|A)P(A)+P(G|A')P(A')}\\\\[/tex]

[tex]=\dfrac{0.23\cdot\dfrac{1}{27}}{0.23\cdot\dfrac{1}{27} + 0.07\cdot\dfrac{26}{27}}\\\\=\dfrac{0.0085185}{0.0759259}\\\\=0.112195\approx0.1122[/tex]

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

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