$A$ game consists of tossing a coin $3$ times and noting its outcome. $A$ boy wins the game if all tosses give the same outcome (i.e.,three heads or three tails) and loses the game otherwise. The probability that the boy loses the game is

When two dice are thrown,the probability of getting the sum of the values on them as $10$ or $11$ is

$A$ number $n$ is chosen at random from $\{1, 2, 3, 4, \ldots, 1000\}$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is:

An unbiased dice with faces marked $1, 2, 3, 4, 5,$ and $6$ is rolled four times. Out of the four face values obtained,the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$ is: (in $/ 81$)

An integer $x$ is chosen at random from $1$ to $50$. The probability that $x + \frac{336}{x} \leq 50$ 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: