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Answer 1

Parameters for $P(Y=1)$
$Y$ is boolean: 2 possible values ( 0 or 1 ).
Estimate $P(Y=1)$.
$P(Y=0)$ is derived as $1-P(Y=1)$.
$1$ parameter for $P(Y=1)$.

Parameters for $P\left(X_1, X_2, X_3 \mid Y=1\right)$
$-X_1, X_2, X_3$ are boolean: $2^3=8$ combinations.
Probabilities must sum to 1 , so estimate $2^3-1$ parameters.
$7$ parameters for $P\left(X_1, X_2, X_3 \mid Y=1\right)$.
Parameters for $P\left(X_1, X_2, X_3 \mid Y=0\right)$
Same process as $P\left(X_1, X_2, X_3 \mid Y=1\right)$.

Estimate 7 parameters for $Y=0$.

$\text{Total parameters :}$

\begin{aligned}
& 1 \text { parameter for } P(Y=1) . \\
& 2^3-1 \text { parameters for } P\left(X_1, X_2, X_3 \mid Y=1\right), \\
& 2^3-1 \text { for } P\left(X_1, X_2, X_3 \mid Y=0\right) .
\end{aligned}

$1+2\left(2^3-1\right)=15$

$\text { Total: } 15 \text { parameters. }$
 

Comments

You are assuming naive bayes classifier, so the features are conditionally independent.

Therefor you have to calculate 1 parameter for P(Y).  

2 parameter for p(x|Y=0) and p(x|Y=1)

2 parameter for p(y|Y=0) and p(x|Y=1)

2 parameter for p(z|Y=0) and p(x|Y=1)

Finally 1+2+2+2=7 parameters overall.