A bag contains 4 balls. Let E be an event in which two balls are drawn at random and found to be white, then

Match List-I with List-II

List-I	List-II
(A) Probability that all balls are white	(I) $\dfrac{1}{6}$
(B) Probability of drawing 2 white ball at random given that there are 3 white ball	(II) $\dfrac{3}{5}$
(C) P(E)	(III) $\dfrac{1}{2}$
(D) Probability of drawing 2 white ball at random given that there is only 2 white ball	(IV) $\dfrac{5}{9}$

Choose the correct answer from the options given below:

The probability that A hits a target is $\frac{1}{5}$ and the probability that B hits it is $\frac{2}{3}$. The probability that the target will be hit if both A and B shoot at it independently is:

Let E and F be two events such that $P(E) = \frac{1}{3}$, $P(F) = \frac{1}{4}$ and $P(E \cap F) = \frac{1}{5}$. Then the value of $P(F|E)$ is equal to

Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is

For any events A and B of a sample space S, which of the following statements are TRUE?

(A) $P(S | B) = 1$

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

(C) $P(\bar{A} | B) = 1 - P(A | B)$

(D) $P(A | B) = \frac{P(A \cap B)}{P(B)}, P(B) \neq 0$

Choose the correct answer from the options given below:

It is known that 3% of plastic bags manufactured in a factory are defective. Using the Poisson distribution on a sample of 100 bags, the probability of at most one defective bag is:

The probability distribution of a random discrete variable is given

If it is known that P(X=1) is the mean of P(X=0) and P(X=2).

Then the value of r is :