A bag contains 5 white, 4 black and 3 red balls. Which of the following statements are True?

A. The probability of drawing three red balls one by one without replacement is $\frac{1}{220}$

B. One by one three balls drawn without replacement then probability that third ball is red is $\frac{1}{4}$

C. The probability of drawing 2 white balls one by one without replacement is $\frac{3}{4}$

D. One by one 3 balls are drawn without replacement then probability that third ball is red is $\frac{3}{4}$

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A random variable X has the following probability distribution:

then, which of the following is correct?

For any events A and B of a sample space S, which of the following statements are TRUE?

(A) $P(S | B) = 1$

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

(C) $P(\bar{A} | B) = 1 - P(A | B)$

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

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The probability that exactly one of them complete the task on time is

Two numbers are selected without replacement at random, one at a time from the first six positive integers. Let x denotes the larger of the two numbers.

Match List-I with List-II

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Let x denote the number of doublets in three throws of a pair of dice with the following probability distribution.

If value of k is equal to $\frac{m}{n} \cdot \gcd(m,n) = 1$, then $m + n$ is equal to

The probability that exactly two of them complete the task on time is