$U_1, U_2, U_3$ are three urns. $U_1$ contains 5 red, 3 white, 2 back balls: $U_2$ contains 4 red 4 white, 2 black balls and $U_3$ contains 3 red. 4 white, 3 black balls. If a ball is chosen at random from an urn chosen at random, then the probability of not getting a black ball is

If the probability distribution of a random variable $X$ is as follows, then $P(X \leq 2)=$

$$ \begin{array}{cccccc}\hline x_i & 0 & 1 & 2 & 3 & 4 \\ \hline P\left(X=x_i\right) & 3 k & 5 k & 3 k^2 & 4 k^2+k & 3 k^2 \\ \hline \end{array} $$

If $X$ follows poisson distribution with variance 2 , then $P(X \geq 3)=$

A straight line passing through a fixed point $(2,3)$ intersects the coordinate axes at points $P$ and $Q$. If $O$ is the origin and $R$ is a variable point such that $O P R Q$ is a rectangle, then the locus of $R$ is