The event $A$ is independent of itself if and only if $P(A) = $

$A$ coin is tossed $3$ times. The probability of obtaining at least two heads is

If $P(A) = P(B) = x$ and $P(A \cap B) = P(A' \cap B') = \frac{1}{3}$,then $x = $

If a die is thrown twice,what is the probability of getting $4$ at least once?

$A$ 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:

$A$ 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: