Two dice are rolled. Then,the probability that the total score is a prime number is

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

$A$ number $x$ is chosen at random from the set $\{1, 2, 3, 4, ......, 100\}$. Then the probability of the event that the chosen number $x$ satisfies the inequality $\frac{(x - 10)(x - 50)}{(x - 30)} \geqslant 0$ is:

$A$ card is drawn randomly from a pack of $52$ playing cards. The probability that the card drawn is neither an ace nor a king is:

The probability of an impossible event,i.e.,$P(\phi)$,is

$A$ student appears for tests $I$, $II$, and $III$. The student is successful if they pass in tests ($I$ and $II$) $OR$ ($I$ and $III$). The probabilities of the student passing in tests $I$, $II$, and $III$ are respectively $p$, $q$, and $1/2$. If the probability of the student being successful is $1/2$, then: