Given the scenario below; it is a small sample dataset for the student engagement in class routines and a prediction to whether such student will pass or fail a particular course. You're required to apply the decision tree using Entropy and Gain Ratio to determine the factors that most significantly influence the outcome.

Hints $lo{g}_{2}x=\frac{lo{g}_{10}x}{lo{g}_{10}2}$ or simply $\frac{logx}{log2}$ and if it happens you encounter $log0$ set it to $0$

$\backslash$table$[[$Study Hours,Attendance,$\backslash$table$[[$Previous$],[$Grades$]],$Participation,Result$],[$Low$,$Poor,Low,No$,$Fail$],[$Medium$,$Fair,Medium,Yes,Pass$],[$High$,$Good,High,Yes,Pass$],[$Low$,$Good,Low,No$,$Fail$],[$Medium$,$Poor,Medium,No$,$Fail$],[$High$,$Fair,High,Yes,Pass$],[$Low$,$Fair,Low,Yes,Fail$],[$Medium$,$Good,Medium,No$,$Pass$],[$High$,$Poor,High,Yes,Pass$],[$Low$,$Fair,Medium,Yes,Fail$]]$

Repeat question a$)$ using Gini index and gain ratio. Compare the final decision tree you obtain in both a$)$ and here. Is there any difference? If there is or not, explain the reason.

Hints: the steps for computing gain ratio are the same in a$)$ and b$)$ and the splitting information formula remains the same in both cases i$.$e it uses Logarithm. Only the gini index computation differs.