If $A$ and $B$ are two events such that $P(A) = \frac{2}{3}$, $P(B) = \frac{1}{2}$ and $P(A | B) = \frac{2}{3}$, then $P(A' \cup B) + P(A \cup B') = $

If $A$ and $B$ are two events such that $P(A) = 0.7$,$P(B) = 0.4$,and $P(A \cap \overline{B}) = 0.5$,where $\overline{B}$ denotes the complement of $B$,then $P(B \mid (A \cup \overline{B}))$ is equal to:

For two events $A$ and $B$,$P(B) \neq 0$ and $P(A \mid B) = 1$,then . . . . . . .

Suppose that Box-$I$ contains $8$ red,$3$ blue and $5$ green balls,Box-$II$ contains $24$ red,$9$ blue and $15$ green balls,Box-$III$ contains $1$ blue,$12$ green and $3$ yellow balls,and Box-$IV$ contains $10$ green,$16$ orange and $6$ white balls. $A$ ball is chosen randomly from Box-$I$; call this ball $b$. If $b$ is red,then a ball is chosen randomly from Box-$II$; if $b$ is blue,then a ball is chosen randomly from Box-$III$; and if $b$ is green,then a ball is chosen randomly from Box-$IV$. The conditional probability of the event 'one of the chosen balls is white' given that the event 'at least one of the chosen balls is green' has happened,is equal to:

$A$ fair die is rolled. Consider events $E=\{1,3,5\}, F=\{2,3\},$ and $G=\{2,3,4,5\}$. Find $P(E | G)$ and $P(G | E)$.

$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B|A)$,if $A$ is a subset of $B$.