A die is rolled. If the outcome is an odd number, then the probability that the number is prime, is:

If A and B are independent events, then which of the following statements are TRUE?

(A) $P(A \cap B) = P(A).P(B)$

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

(C) $P(A \cup B) = P(A) + P(B) - P(A).P(B)$

(D) $P(A \cap B) = P(A). P(B|A)$

Choose the correct answer from the options given below:

Which of the following are the properties of Normal Distribution function f(x) and Normal probability curve:

(A) The probability of success remains the same in each trial and the number of trials is small in number.

(B) The curve is bell-shaped and is symmetrical about the mean.

(C) If set of n trials are repeated N times, then frequency f(r) of r successes is given by f(r) = N.p(r) = N$e^{-m\frac{m^r}{r!}}$, r=0,1,2,...

(D) As x increases numerically, f(x) decreases rapidly and the maximum value of f(x) occurs at x=μ(mean)

Choose the correct answer from the options given below:

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

60% members of a committee favour a certain proposal and 40% members oppose the proposal. A member is selected and let the random variable X = 0 if he opposes and X = 1 if he is in favour. Then the variance of the random variable X is

Match List-I with List-II

If the random variable x has the following distribution:

Choose the correct answer from the options given below:

In a Binomial distribution, the probability of getting a success is $\frac{3}{4}$ and the variance is $\frac{3}{8}$ then the probability of no success is: