If X is a random variable which can take values 0,1,2,3 such that $E(X^2) = 2E(X)$.

If $P(X=0) = P(X=1) = m\ \&\ P(X=2) = 2m$, then which of the following are TRUE?

A. $P(X=1) = \dfrac{1}{13}$

B. $P(X=3) = \dfrac{1}{13}$

C. $E(X) = \dfrac{18}{13}$

D. $P(X=2) = \dfrac{6}{13}$

Choose the correct answer from the options given below:

On a multiple choice examination with four possible answers (out of which only one is correct) for each of five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Match list I with list II. 4 defective pens are mixed with 10 normal pens. 3 pens are drawn one by one with replacement , then the probability distribution of the number of defective pens is :

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There are 10% defective pens. In a sample of randomly selected 10 pens, the probability that atmost one pen is defective, is

If $X$ is a discrete random variable which assumes values $x_1, x_2, x_3, ..., x_n$ with the respective probabilities $p_1, p_2, ....., p_n$, then

Match the LIST-I with LIST-II

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If the probability distribution of a random variable X is given as

Then the mean of X is

If 0.1% of the bolts manufactured by a machine are found to be defective. Find the probability that, in a sample of 2000 bolts chosen at random, exactly 3 will be defective using the Poisson distribution. [Given $e^{-2} =0.1353$]