From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random. Let X denotes the number of defective items in the sample. If the sample is drawn randomly, then Match List-I with List-II (P(X) denotes the probability of occurence of X)

List-I	List-II
(A) P (X = 0)	(I) $\dfrac{^3C_3\times{}^7C_1}{^{10}C_4}$
(B) P (X = 1)	(II) $\dfrac{^7C_4\times{}^3C_0}{^{10}C_4}$
(C) P (X = 2)	(III) $\dfrac{^3C_1\times{}^7C_3}{^{10}C_4}$
(D) P (X = 3)	(IV) $\dfrac{^3C_2\times{}^7C_2}{^{10}C_4}$

Choose the correct answer from the options given below:

Let A and B be two events such that $P(A \cap B) = 0$ then $P(A|(A \cup B))$ is equal to:

Consider two independent events A and B such that $P(A) = 0.3$, $P(B) = 0.6$.

Match List-I with List-II

Choose the correct answer from the options given below:

The probability distribution of a random variable $x$ is, $P(x) = \frac{k}{2^x}, x = 0, 1, 2, 3$. Then

Match List-I with List-II

Choose the correct answer from the options given below:

If A and B are two events such that $A \neq \emptyset$, B $\neq \emptyset$, then which of following is/are TRUE:

A. $P(B/A)=P(A).P(B)$

B. $P(B/A)=\frac{P(A\cap B)}{P(A)}$

C. $P(A'/B')=\frac{1-P(A\cup B)}{1-P(B)}$

D. $P(B/A).P(A/B)=2$

Choose the correct answer from the options given below:

There are three identical boxes I, II and III, each containing two balls. In box I, both balls are red, In box II, both balls are blue and box III contains one blue ball and one red ball. A boy randomly chooses a box and takes out a ball at random from it. If the ball is red, then the probability that the other ball in the box is also red colour is:

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is: