$1.[3$ pt$.]$ Consider the following data set of ten observations for classification of a binary categorical variable $\backslash ($ Y $\backslash )$ that has two classes $($Yes and No$),$ using two features. $\backslash ($ X$\_\{1\}\backslash )$ takes three possible values: A$,$ B$,$ and C$.\backslash ($ X$\_\{2\}\backslash )$ takes four possible values: $1$st$,2$nd$,3$rd$,$ and $4$th$.$

Which feature $(\backslash ($ X$\_\{1\}\backslash )$ or $\backslash ($ X$\_\{2\}\backslash ))$ contains the information more closely relevant to $\backslash ($ Y $\backslash )?$ Answer it by calculating the following.

a$)$ Entropy of each feature $(\backslash ($ X$\_\{1\}\backslash )$ and $\backslash ($ X$\_\{2\}\backslash ))$

b$)$ Conditional entropy of each feature

c$)$ Information gain of each feature