Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	If $A$ and $B$ are mutually exclusive events then $P(A \cup B) =$	I.	$\dfrac{P(A \cap B)}{P(B)}, P(B) \neq 0$
B.	If $A$ and $B$ are independent events then $P(A \cap B) =$	II.	$\dfrac{P(A \cap B)}{P(A)}, P(A) \neq 0$
C.	If $A$ and $B$ are two events of a sample space of an experiment, then $P(A/B) =$	III.	$P(A) \cdot P(B)$
D.	If $A$ and $B$ are two events of a sample space of an experiment, then $P(B/A) =$	IV.	$P(A) + P(B)$

Choose the correct answer from the options given below:

If A and B are two events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$, then which of the following statements are true?

(A) A and B are independent events

(B) $P(A | B) = \frac{3}{4}$

(C) $P(A' | B') = \frac{5}{8}$

(D) $P(A' | B) = \frac{1}{4}$

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It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability that randomly selected person from a population, not having COVID 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

Choose the correct answer from the options given below:

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:

A problem in mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem is solved is

The standard deviation of the number of tails in three tosses of a coin is: