Consider the following dataset with three Boolean descriptive features $a,b$ and $c$ and a single Boolean

target feature, $K$ :

For the questions below, assume that the naive Bayes classifier is used to predict the value of $K$ from the

values of the other variables.

$($a$)$ According to the Naive Bayes classifier, what is $P(K=1|a=1,b=1,c=0)?$ Show all your

calculations.

$($b$)$ According to the Naive Bayes classifier, what is $P(K=0|a=1,b=1)?$ Make sure to show all your

calculations.

Given the Bayes network below, for each of the questions that follow, compute the probabilities. Show all

vour calculations.

$($a$)P(A|B)$

$($b$)$ AML$874$: $P(B|D)$

$($c$)P(C|B)$

Suppose that a naive Bayes classifier is used to learn a classifier for $y=$A and $B,$ where A and $B$ are

independent of each other, and are Boolean descriptive features with $P(A)=0\mathrm{.}4$ and $P(B)=0\mathrm{.}5.$

Draw the Bayesian network that represents the independence assumptions fo the classifier and fill in the

probability tables for the network. Show all your calculations.