If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A \cup B).$

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

Bag $A$ contains $9$ white and $8$ black balls, while bag $B$ contains $6$ white and $4$ black balls. One ball is randomly picked up from bag $B$ and mixed with the balls in bag $A$. Then a ball is randomly drawn from bag $A$. If the probability that the ball drawn is white is $p/q$ (where $gcd(p,q)=1$), then $p+q$ is equal to:

If $P(AB) = P(A)P(B)$,$P(A/B) = 1/4$,and $P(B/A) = 1/3$,then which of the following is true?

If $2 P(A) = P(B) = \frac{5}{13}$ and $P(A \mid B) = \frac{2}{5}$,then $P(A \cup B) = $ . . . . . . .

Let $X$ and $Y$ be two events of a sample space such that $P(X)=\frac{1}{3}$, $P(X|Y)=\frac{1}{2}$ and $P(Y|X)=\frac{2}{5}$, then which of the following is true?