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

$A$ family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

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:

$A$ die is thrown three times and the sum of the numbers obtained is $15$. What is the probability that the number $4$ appears in the first throw?

Given that $E$ and $F$ are events such that $P(E)=0.6$,$P(F)=0.3$,and $P(E \cap F)=0.2$,find $P(E|F)$ and $P(F|E)$.

If $E$ and $F$ are events such that $P(\overline{F}) = 0.7$ and $P(E \cap F) = 0.2$,then $P(E \mid F)$ is