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

Fifteen football players of a club-team are given $15$ $T$-shirts with their names written on the backside. If the players pick up the $T$-shirts randomly,then the probability that at least $3$ players pick the correct $T$-shirt is

If $P(A') + P(B') P(A \cup B) = 0.7$,then $P(A') + P(B')$ is

$A$ pair of fair dice is rolled together till a sum of either $5$ or $7$ is obtained. Then the probability that $5$ comes before $7$ is

In a random experiment,a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

Two persons $A$ and $B$ take part in a shooting competition. $A$ can hit the target with a probability of $0.6$. $B$ can hit the target with a probability of $0.8$. $A$ takes the first shot,after which they shoot alternately. The probability that $A$ wins the competition is