If $A$ and $B$ are events such that $P(A \cup B) = 3/4,$ $P(A \cap B) = 1/4,$ and $P(\bar{A}) = 2/3,$ then $P(\bar{A} \cap B)$ is

Three identical dice are rolled. The probability that the same number will appear on each of them is:

Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. Then the probability that $a^2 - b^2$ is divisible by $3$ is (in $/87$)

If $A, B, C$ are three events of a sample space such that $P(B)=\frac{3}{2} P(A)$ and $P(C)=\frac{1}{2} P(B)$, then which of the following is correct?

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

$A$ 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