Let X denote the number of hours a person watches television during a randomly selected day. The probability that X can take the value $x_i$, has the following form, where $k$ is some unknown constant.

$P(X=x_i) = \begin{cases} 0.5 & \text{if } x_i=0 \\ kx_i & \text{if } x_i=1 \\ k(4-x_i) & \text{if } x_i=2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$

The probability that the person watches at most 2 hours of television on a selected day is :

A beg contains 4 white and 6 red balls. Four balls are drawn at random, then match the probability of the numbers of white balls drawn. Where P(E) denotes the probability of an event E.

Then Match List-I with List-II

Choose the correct answer from the options given below:

Let the random variable X represent the positive difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. Then probability $P(X \leq 3)$ is equal to

If A and B are two events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$, $P(B|A) = \frac{1}{4}$, then $P(A|B)$ is:

For any two events A and B, which of the following are correct?

(A) $P(A\cup B) = P(A)+P(B)-P(A\cap B)$

(B) $P(A) = P(A\cup B)+P(A\cap B)$

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

(D) $P(A) = P(A\cap B)+P(A\cap \bar{B})$

Choose the correct answer from the options given below:

Two events A and B will be independent, then

The probability that in a year of the 22nd century choosen at random, there will be 53 Sundays is: