(Round off to three decimal places)

The naive Bayes classifier is used to solve a two-class classification problem with class labels $y_1, y_2$. Suppose the prior probabilities are $P\left(y_1\right)=\frac{1}{3}$ and $P\left(y_2\right)=\frac{2}{3}$. Assuming a discrete feature space with $P\left(x \mid y_1\right)=\frac{3}{4}$ and $P\left(x \mid y_2\right)=\frac{1}{4}$ for a specific feature vector $x$. The probability of misclassifying $x$ is

_________ (Round off to two decimal places)

Let $\left\{x_1, x_2, \ldots ., x_n\right\}$ be a set of linearly independent vectors in $\mathbb{R}^n$. Let the $(\mathrm{i}, \mathrm{j})$ - th element of matrix $A \in \mathbb{R}^{n \times n}$ be given by $A_{i j}=x_i^T x_j, 1 \leq i, j \leq n$. Which one of the following statements is correct?

Consider the neural network shown in the figure with inputs: $u, v$ weights: $a, b, c, d, e, f$ output: $y$ R denotes the ReLU function, $\mathrm{R}(x)=\max (0, \mathrm{x})$.

Given $u=2, v=3$, $a=1, b=1, c=1, d=-1, e=4, f=-1$, which one of following is correct?

Consider game trees Tree-1 and Tree-2 as shown. The first level is a MAX agent and the second level is a MIN agent. The value in the square node is the output of the utility function.