Urn I contains 6 red balls and 4 black balls and Urn II contains 4 red balls and 6 black balls. One ball is drawn at random from Urn I and placed in Urn II. If one ball is drawn at random from Urn II, then the probability that it is a red ball is :

Which of the following statements are correct?

(A) The mean and variance of the Poisson distribution are equal.

(B) The mean and variance of a Binomial distribution are equal.

(C) An unbiased die is thrown again and again until two sixes are obtained, then the probability of obtaining the second six in the 3rd throw is $\frac{5}{108}$.

(D) If the variance of a Poisson distribution is 2, then P(X = 2) = $2e^{-2}$

Choose the correct answer from the options given below:

If $P(A) = \frac{3}{10}$, $P(B) = \frac{2}{5}$ and $P(A \cup B) = \frac{3}{5}$ then the value of $P(B|A) + P(A|B)$ is:

If A and B are any two events such that P(B) = P(A and B), then which of the following is correct

If a person A speaks the truth in 80% cases and the person B speaks the truth in 75% cases, then the probability that they contradict each other in a statement is

When the doctor arrives late, what is the probability that he comes by other means of transport?

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: