For two events $A$ and $B$,if $P(A) + P(B) - P(A \cap B) = P(A)$,then . . . . . . .

$A$ couple has two children. One of them is a boy. What is the probability that the other child is also a boy?

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

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:

Let $A, B, C$ be pairwise independent events such that $P(C) > 0$ and $P(A \cap B \cap C) = 0$. Then $P(A' \cap B'|C)$ is equal to:

If two events $A$ and $B$ are such that $P(\overline{A}) = 0.3$,$P(B) = 0.4$,and $P(A \cap \overline{B}) = 0.5$,then $P(B | (A \cup \overline{B})) = $