Probability of solving a specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ respectively, then which of the following are True?

[where P(X) denotes the probability of an event X]

(A) P(Problem is solved) = $\frac{2}{3}$

(B) P(Exactly one of them solves the problem) = $\frac{1}{2}$

(C) P(Both of them solve the problem) = $\frac{5}{6}$

(D) P(Atmost one solves the problem) = $\frac{5}{6}$

Choose the correct answer from the options given below:

A random variable X has the following probability distribution:

The value of E(X) is:

If A and B are two independent events such that P(A) = 1/3, $P(A\cup B) = 3/5$ and P(B) = p, then which of the following are true?

(A) The value of p is $\frac{2}{5}$

(B) $P(A\cap B) = \frac{2}{15}$

(C) $P(B/A) = \frac{1}{3}$

(D) $P(A/B) = \frac{3}{5}$

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 selected person will be diagonosed as COVID positive is :

Two numbers are selected at random from the integers 1 through 19. If the sum is even, then the probability that both are odd numbers is:

Two dice are thrown simultaneously. If X denotes the number of sixes, then the mean of X is :

In a Binomial distribution, the probability of getting a success is $\frac{3}{4}$ and the variance is $\frac{3}{8}$ then the probability of no success is: