Match List-I with List-II

List-I	List-II
(A) $P(A \cap B) = P(A).P(B)$	(I) $\frac{P(B \cap A)}{P(A)}, P(A) \ne 0$
(B) $\frac{P(S \cap B)}{P(B)}$, S = Sample space	(II) A, B are independent events
(C) $P(B/A) =$	(III) $P(\bar{A} \cap \bar{B})$
(D) $P(\overline{A \cup B})$	(IV) 1

Choose the correct answer from the options given below:

Let $F(z)$ be the cumulative density function of the standard normal variate $z$, then which of the following are correct?

(A) $F(z) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^z e^{-\frac{z^2}{2}} dz$, $-\infty < z < \infty$

(B) $F(-z) = 1 - F(z)$

(C) $F(0) = 0$

(D) $F(\infty) = 1$

Choose the correct answer from the options given below:

Let X be the random variable with probability distribution given by the following table.

The value of $P(X \leq 1)$ is:

A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$. They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.

The probability that seed will not germinate, given that the seed is of type $A_3$.

Urn I contains 6 red balls and 4 black balls and Urn II contains 4 red balls and 6 black balls. One ball is drawn at random from Urn I and placed in Urn II. If one ball is drawn at random from Urn II, then the probability that it is a red ball is :

Match List-I with List-II

Let A & B are two events such that P(A)=0.8, P(B)=0.5, P(B|A)=0.4

Choose the correct answer from the options given below:

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probability, that both coins are unbiased is: