A random variable X has the following probability distribution:

X	0	1	2	3	4	5	6
P(X)	K	3K	7K	5K	4K	K	2K

The value of K is

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is:

Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice.

Match List-I with List-II

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If a computer code is correctly programmed, it gives 90% acceptable results. But if it is not correctly programmed, it gives only 40% acceptable results. From previous experience, it is observed that only 80% of codes are correctly programmed. If after a certain programming, the code gives 2 acceptable results, then the approximate probability that the code is correctly programmed is

If A and B are two distinct events such that P(A|B) = P(B|A), then which of the following is /are possible?

(A) A= B

(B) P (A) = P(B)

(C) A ⊂ B but A ≠ B

(D) A∩ B = ɸ

Choose the correct answer from the options given below:

Match List-I with List-II

Let $A$ and $B$ be two events such that $P(A) = 0.2$, $P(B) = 0.4$, $P(B|A) = 0.5$

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If $A$ and $B$ are independent events such that $0 < P(A) < 1$ and $0 < P(B) < 1$, then identify the correct statements.

(A) $A$ and $B'$ are independent

(B) $A'$ and $B$ are independent

(C) $A$ and $B$ are mutually exclusive

(D) $A'$ and $B'$ are independent

Choose the correct answer from the options given below :