In Binomial distribution with parameters $n = 12$ and $p = \frac{1}{3}$, value of $E(X^2) + E(X)$ is :

A coin is tossed four times. The probability of getting atleast 1 head before getting the first tail is

Three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls. Let X denote the number of white balls.

Match the LIST-I with LIST-II

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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:

If an unbiased coin is tossed 10 times, probability of obtaining more head than tail is :

Probability that a man speaks truth is $\frac{3}{4}$. He throws a die and reports that it is a six. The probability that it is actually a six is

Let A and B be two events. Then which of the following statements are TRUE?

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

(B) $P(B') = 1 + P(B)$

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

(D) $P(A \cap B) = P(A).P(B)$ If A and B are independent events

Choose the correct answer from the options given below: