If a random variable X follows binomial distribution with mean $\dfrac{4}{3}$ and variance $\dfrac{8}{9}$. Which of the following are correct?

A. Probability of success is $\dfrac{1}{3}$.

B. Probability of failure is $\dfrac{2}{3}$.

C. Number of trials is 4.

D. $P(X \ge 1) = \dfrac{35}{81}$

Choose the correct answer from the options given below:

There are 50 telephone lines in an exchange. If the probability that any one of them will be busy is 0.1, then the probability that all the lines are busy is

Let X denote the number of scores in a test. If X is normally distributed with mean 100 and standard deviation 15, then the probability that X does not exceed 130 is,

(Given $P(0 \le Z \le 2)=0.4772$, where $Z$ be the standard normal variate)

In a random experiment, a collection of trials is called Bernoulli trials then which of the following statements are TRUE?

A. The number of trials is infinite.

B. Each trial has exactly two outcomes defined as success and failure.

C. The trials are dependent by nature.

D. The probability of success remains the same in each trial.

Choose the correct answer from the options given below:

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If $P(X=1) = 0.4$, $P(X=4) = P(X=2)$ and $P(X=3) = 2P(X=2)$, then $P(X=0)$ is :

Let the random variable $X$ follow a Poisson distribution. If $P(X=3)=\dfrac{2}{5}P(X=2)$, then $P(X=1)$ is equal to

The probability distribution of a random variable X is given as:

$P(X=x) = \begin{cases} kx^2 & for & x=1,2,3 \\ 2kx & for & x=4,5,6 \\ 0 & otherwise \end{cases}$

Where $k$ is an arbitrary constant, then $E(X)$ is equal to: