Problem $1.$ Consider the training examples in the table shown in Fig. $1.$

$($a$)$ Estimate the conditional probabilities for $P(A|+),P(B|+),P(C|+),P(A|-),P(B|-),$ and $P(C|-).$

$($b$)$ Use the estimate of conditional probabilities given in the previous question to predict the class label for a test sample $(A=0,B=1,C=0)$ using the naive Bayes approach

$($c$)$ Read section $6\mathrm{.}4$ of TSKK $($international version$)$ or section $4\mathrm{.}4$ of TSKK $($US version$)$ to understand how to use $m-$estimate to handle zero conditional probabilities.

$($d$)$ Estimate the conditional probabilities using the $m-$estimate approach, with $p=\frac{1}{2}$ and $m=4.$

$($e$)$ Repeat part $(b)$ using the conditional probabilities given in part $(c).$

$($f$)$ Compare the two methods for estimating probabilities. Which method is better and why?

$\backslash$table$[[$Instance$,A,B,C,$Class$],[1,0,0,0,+],[2,0,0,1,-],[3,0,1,1,-],[4,0,1,1,-],[5,0,0,1,+],[6,1,0,1,+],[7,1,0,1,-],[8,1,0,1,-],[9,1,1,1,+],[10,1,0,1,+]]$

Figure $1$: Binary Classification Problem