If $l, m$ represent any two elements (identical or different) of the set $\{1,2,3,4,5,6,7\}$, then the probability that $l x^2+m x+1>0 \forall x \in R$ is

$A$ and $B$ are playing chess game with each other. The probability that $A$ wins the game is 0.6 . the probability that he loses is 0.3 and the probability its draw is 0.1 . If they played three games, then the probability that $A$ wins atleast two games is

$U_1, U_2, U_3$ 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 $P(X \leq 2)=$

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