If $P(E)=0.8, P(F)=0.5$ and $P(F \mid E)=0.4$ then,$P(E \mid F)=$ . . . . . . .

$A$ coin is tossed three times. If event $E$ represents getting at least two heads and event $F$ represents getting a head on the first toss,find $P(E|F)$.

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:

$A$ black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than $9,$ given that the black die resulted in a $5$.

Two cards are drawn from a pack of $52$ playing cards one after the other. If $p_1$ is the probability of getting a queen in the first draw and a diamond card in the second draw when the first card drawn is replaced, and $p_2$ is the probability of the same event when the first card drawn is not replaced, then $\frac{p_1}{p_2} = $

$P(A / A \cap B) + P(B / A \cap B) =$