Bag $A$ contains 4 white and 2 black balls, bag $B$ contains 3 white and 3 black balls and bag $C$ contains 2 white and 4 black balls. If a bag is chosen at random and a ball is chosen at random from it, then the probability that the ball drawn is black is

A random variable $X$ has the following probability distribution

$$ \begin{array}{llllllllll} \hline X=\mathbf{x}_i & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline P\left(X=\mathbf{x}_i\right) & 10 k & 9 k & 8 k & 8 k & 6 k & 5 k & 4 k & 3 k & k \\ \hline \end{array} $$

where $k$ is a real number.

If $A=\left\{x_i \mid x_i\right.$ is a prime number $\}$ and $B=\left\{x_i \mid x_i>5\right\}$ are two events, then $P(A \cup B)=$

If $X$ is a Poisson variate such that $\frac{5}{3} k=P(X=2) =P(X=3)$, then $P(X=5)=$

A bag contains 9 identical black balls numbered 1 to 9 . and 4 identical white balls numbered 1 to 4 . If 3 balls are drawn at a time randomly from that bag, then the probability of getting atleast one white ball is