GATE DA 2025 Q35: Naive Bayes: probability of misclassifying x

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 $P(y_1) = \frac{1}{3}$ and $P(y_2) = \frac{2}{3}$. Assuming a discrete feature space with

$$P(x|y_1) = \frac{3}{4} \quad \text{and} \quad P(x|y_2) = \frac{1}{4}$$

for a specific feature vector $x$. The probability of misclassifying $x$ is ____ (Round off to two decimal places)