A random variable X has the following probability distribution:

x	1	2	3	4
p(x)	2k	4k	3k	k

The value of E(X) is:

If A and B are event such that $P(A)=\dfrac{1}{2}$, $P(B)=p$ and $P(A \cup B)=\dfrac{3}{5}$ then which of following statements is/are TRUE?

(A) Events A and B are independent if $p=\dfrac{1}{5}$

(B) Events A and B are independent if $p \in (0,1) \sim \left\{\dfrac{1}{5}\right\}$

(C) Events A and B are independent then $P(A \cap B)=\dfrac{1}{10}$

(D) Event A and B are independent then $P(A \cap B)=\dfrac{9}{10}$

Choose the correct answer from the options given below:

A fair coin is tossed a fixed number of times. If the probability of getting 11 heads is equal to the probability of getting 13 heads, then the probability of getting 2 heads is:

Bag I contains 3 black and 2 white balls. Bag II contains 2 black and 4 white balls. A bag is selected at random and then a ball is drawn from it. The probability that the ball drawn is black is:

A random variable $X$ has the following probability distribution:

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

A die is tossed once. If the random variable X is defined as $X = \begin{cases} 1, & \text{if the die result in an odd number} \\ -1, & \text{if the die result in an even number} \end{cases}$, then the variance of X is

A coin is tossed 7 times. The probability of getting at least 4 heads is: