Match List-I with List-II

List-I	List-II
(A) For a random variable X, $E(X)=3$ and $E(X^2)=11$, then $Var(X)$ is	(I) 25
(B) For a random variable X, $E(X)=3$ and $E(X^2)=13$, then $Var\left(\frac{X}{2}\right)$ is	(II) 2
(C) In a binomial distribution, if $n=20, q=0.75$, then its mean is	(III) 1
(D) If in a binomial distribution, mean is 5 and variance is 4, then the number of trials is	(IV) 5

Choose the correct answer from the options given below:

A lot of 50 watches is known to have 10 defective watches. If 8 watches are selected one by one with a replacement at random, then the probability that there will be at least one defective watch is:

The random variable X has the following probability distribution:

The correct value of k is:

If in a binomial distribution $n = 4$, $P(X=0) = \frac{16}{81}$, then $P(X=4)$ equals :

A random variable X has the following probability distribution:

The value of K is

A company has two plants $P_1$ and $P_2$ which produces 60% and 40% of pens respectively. At plant $P_1$ 80% of pens are rated of grade A and at plant $P_2$ 90% of pens are rated of grade A. A pen is picked up at random and is found to be of grade A. The probability that it has manufactured from plant $P_1$ is:

It is given that student marked the answer correctly, the probability that he guesses is