If A and B are two events such that $P(A) = \dfrac{3}{10}, P(B) = \dfrac{2}{5}$ and $P(A \cup B) = \dfrac{3}{5}$, then $P(B|A) + P(A|B)$ is:

The random variable X has the following probability distribution:

The correct value of k is:

The probability that he copied it given that his answer is correct :

Match the options of List-I to List-II :

Choose the correct answer from the options given below :

If A and B are two events such that $A \neq \emptyset$, B $\neq \emptyset$, then which of following is/are TRUE:

A. $P(B/A)=P(A).P(B)$

B. $P(B/A)=\frac{P(A\cap B)}{P(A)}$

C. $P(A'/B')=\frac{1-P(A\cup B)}{1-P(B)}$

D. $P(B/A).P(A/B)=2$

Choose the correct answer from the options given below:

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:

If the sum and difference of squares of mean and variance of a Binomial distribution is $\frac{225}{256}$ and $\frac{63}{256}$ respectively, the $P(X \geq 2)$ is: