Two dice are thrown simultaneously. If X denotes the number of sixes appearing on two dice, then which of the following are correct?

(A) $P(X=0)=\frac{1}{36}$

(B) $P(X=1)=\frac{10}{36}$

(C) $P(X=1)+P(X=0)=\frac{35}{36}$

(D) $P(X=1)+P(X=2)=\frac{11}{36}$

Choose the correct answer from the options given below:

The probability distribution of a random variable X is given by

If $a > 0$, then $P(0 < x \leq 2)$ is equal to

If a random variable y follows Poisson's distribution such that $P(X = 2) = 9 P(X = 4) + 90 P(X = 6)$, then sum of the mean and variance of X is

A fair coin is tossed 100 times. The probability of getting head an odd number of times is

The mean of the number of heads in a simultaneous toss of three coins is

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Then, E (X) is :

The random variable X has a probability distribution P(X) of the following form, where k is some number.

$P(X=x) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$

Then $P(x \leq 2)$ is :