Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. The probability distribution of the number of kings will be:

If $2P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$, then $P(A \cap B)$ is

Urn A contains 1 white, 2 black and 3 red balls, Urn B contains 2 white, 1 black and 1 red ball and Urn C contains 4 white, 5 black and 3 red balls. One Urn is chosen at random and two balls are drawn. If it is found that there is one white and one red, Then the probability that they come from A is:

The probability that task is completed on time by at least one of them 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:

If X is a random variable and a, b are real numbers, then which of the following statements are correct?

(A) $E[aX+b] = a E(X) + b$

(B) $Var (aX + b) = a^2 Var (X) + b$

(C) $Var (aX + b) = a Var (X)$

(D) $Var (X) = E(X^2) - [E(X)]^2$

Choose the correct answer from the options given below:

A card is picked at random from a pack of 52 playing cards. If the picked card is a queen, then probability of card to be of spade type also, is