Answer
The probability of snowing in Greenland when glaciers are growing is approximately $0.1724$
Work Step by Step
According to Bayes' theorem:
$P(S|G)=\dfrac{P(G|S)P(S)}{P(G|S)P(S)+P(G|S')+P(S')}~~~~~~~~(1)$
Here, we have
$P(G|S)= 20 \% =0.2 \\ P(S)= \dfrac{1}{25} \% =0.04 \\ P(G|S')=4 \% =0.04$
Now, we will now use formula (1) and the given data to obtain:
$P(S|G)=\dfrac{P(G|S)P(S)}{P(G|S)P(S)+P(G|S')+P(S')}=\dfrac{(0.2)(0.04)}{(0.2)(0.04)+(0.04) (1-0.04)}$
or, $ \approx 0.1724$
Thus, we conclude the probability of snowing in Greenland when glaciers are growing is approximately $0.1724$.
