If the probability distribution of a random variable X is as given below :

X	-1	0	1	2	3
P(X)	K	$\frac{1}{5}$	2K	$\frac{3}{10}$	K

Then the value of K is :

If $X$ is a random variable which can assume values $0, 1, 2, 3$ or $4$ such that $P(X = 1) = P(X = 2)$ and $3P(X = 3) = 4P(X = 4) = P(X = 0) = \frac{1}{8}$, then $P(X > 0)$ is:

If A and B are two independent events, then which of the following is/are true?

(A) $P(A \cap B) = 0$

(B) $P(A \cup B) = 1 - P(A')P(B')$

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

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

Choose the correct answer from the options given below:

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001. The probability that out of 2000 individuals, more than two individuals suffer from bad reaction is:

[Given that $e^{-2} \approx 0.13534$]

A man speaks the truth 8 out of 10 times. A die is tossed. He reports that it was 5. What is the probability that it was actually 5?

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 :

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X denotes the number of Spades in two draws, then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below: