For a random variable x, probability distribution P(x) is given by $P(x) = \frac{k}{6}(3-x), x = 0, 1, 2$, then

Match List-I with List-II

List-I	List-II
(A) k is equal to	(i) $\frac{1}{2}$
(B) P(x = 0)	(ii) 1
(C) P(x < 2)	(iii) $\frac{1}{6}$
(D) P(1 < x ≤ 2)	(iv) $\frac{5}{6}$

Choose the correct answer from the options given below:

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability that the person is actually having COVID given that he is tested as COVID positive is :

Bag I contains 2 red and 3 blue balls and bag II contains $\alpha$ red and 5 blue balls. One ball is drawn at random from one of the bags and is found to be blue. If the probability that it was drawn from bag II is $\frac{25}{52}$, then $\alpha$ is equal to:

If A and B are independent events, then which of the following is/are true?

(A) $\bar{A}$ and B are independent events

(B) $P(A \cap B) = 0$

(C) $\bar{A}$ and $\bar{B}$ are independent events

(D) $P(A \cap B) = P(A) + P(B)$

Choose the correct answer from the options given below:

Probability that a man speaks truth is $\frac{3}{4}$. He throws a die and reports that it is a six. The probability that it is actually a six is

A problem in mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem is solved is

If the mean and variance of a binomially distributed random variable X are 4 and 2 respectively, then $P(X = 2)$ is equal to