Q1)
# - (9/12) (log(9/12)/log2) - (3/12) (log(3/12)/log2)

# = 0.8113


Q2)
Cloudy, because:
1)visually, it has the most matching datapoints
2)visually, the "yes" option for cloudy is guaranteed to eliminate "yes" results from rain
3)mathematically, it has the lowest entropy, in which it creates the highest information gain:
 entropy for (x|rain):
 Temperature (split 25-27|28-29): 0.9080
 Temperature (split 25-26|27-29): 0.8755
 UV Index: 0.8333
 Humidity: 0.8333
 Cloudy: 0.5732 *

Q3)
		Rain
		Yes	No	Total	P(Clou)	E	P*E
Cloudy	Yes	3	0	3	0.25	0	0
        No	2	7	9	0.75	0.7 0.5
				12
Entropy  =	0.5731

# Information Gain = 0.4067