A clinic specializes in testing for a disease D. The result of the test can be either positive or negative.

A study revealed that if a person suffers from the disease D, the test result in that clinic comes out positive 80% of the time, and negative 20% of the time. If a person is not suffering from the disease D, the test comes out positive 10% of the time and negative 90% of the time. It is also known that among the general population, the disease D occurs in 30% of the individuals.

If a person tests positive for D in that clinic, the probability that he/she actually suffers from the disease D is __________ . (Rounded off to two 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 $P(y_1)=\frac{1}{3}$ and $P(y_2)=\frac{2}{3}$. Assuming a discrete feature space with

$$P(x|y_1)=\frac{3}{4}$$ and $$P(x|y_2)=\frac{1}{4}$$ for a specific feature vector $x$. The probability of misclassifying $x$ is
(Round off to two decimal places)

There are three boxes containing white balls and black balls.

Box-1 contains 2 black and 1 white balls.
Box-2 contains 1 black and 2 white balls.
Box-3 contains 3 black and 3 white balls.

In a random experiment, one of these boxes is selected, where the probability of choosing Box-1 is $\frac{1}{2}$, Box-2 is $\frac{1}{6}$, and Box-3 is $\frac{1}{3}$. A ball is drawn at random from the selected box. Given that the ball drawn is white, the probability that it is drawn from Box-2 is
(Round off to two decimal places)

Consider two events T and S. Let $\overline{T}$ denote the complement of the event T. The
probability associated with different events are given as follows:
$$P(\overline{T})=0.6,P(S|T)=0.3,P(S|\overline{T})=0.6$$
Then, $P(T|S)$ is ______ (rounded off to two decimal places).