If $A$ and $B$ are any two events,then $P(\bar{A} \cap B) = $

In a single throw of two dice,the probability of getting a sum of more than $7$ is

When two dice are thrown simultaneously,what is the probability that the sum of the numbers on the top faces is $5$?

$A$ random experiment has five outcomes $w_1, w_2, w_3, w_4$ and $w_5$. The probabilities of the occurrence of the outcomes $w_1, w_2, w_3, w_4$ and $w_5$ are respectively $\frac{1}{6}, a, b, c$ and $\frac{1}{12}$ such that $12a + 12b - 1 = 0$. If $p(w_4) = c$ and the outcomes are equally likely for $w_2, w_3, w_4$,find the probability of the outcome $w_3$. Given the condition $12a + 12b = 1$,and assuming $a=b=c$ for the remaining outcomes,find $p(w_3)$.

$A$ bag contains $7$ green and $5$ black balls. $3$ balls are drawn at random one after the other. If the balls are not replaced,then the probability of all three balls being green is

If a number $x$ is drawn randomly from the set of numbers $\{1, 2, 3, \ldots, 50\}$,then the probability that the number $x$ satisfies the inequation $x + \frac{10}{x} \leq 11$ is