If the random variable X is normally distributed with mean 16 and standard deviation 4, then the standard normal variable Z corresponding to X = 17 is

The binomial distribution for which the mean is 5 and variance 4, is

Two events A and B will be independent, then

For any two events A and B, which of the following are correct?

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

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

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

(D) $P(A) = P(A\cap B)+P(A\cap \bar{B})$

Choose the correct answer from the options given below:

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Then, E (X) is :

If the random variable $X$ has the following distribution:

Match List-I with List-II:

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 is of type $A_1$ given that seed doesn't germinate.