Bag A contains 2 red and 3 white balls, Bag B contains 3 red and 2 white balls. If a ball is drawn at random and is found to be red, then the probability that it was drawn from bag B, 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:

If three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls, then the probability distribution of the number of white balls drawn is

Let A and B be two independent events such that $P(A)=k$, $P(B)=2k$ and probability of occurrence of exactly one of them is $\dfrac{5}{9}$. Then the value(s) of $k$ is/are:

If a random variable X has the following probability distribution:

then,

Match List-I with List-II

Choose the correct answer from the options given below:

The probability distribution of a random variable $x$ is, $P(x) = \frac{k}{2^x}, x = 0, 1, 2, 3$. Then

Match List-I with List-II

Choose the correct answer from the options given below:

The value of $k$ is