$A$ 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 $P(E|F)$.

If $P(A / B) = \frac{3}{10}$,$P(B / A) = \frac{4}{5}$ and $P(A \cup B) = K P(B)$,then $\frac{1}{K} =$

If $E$ and $F$ are two independent events with $P(E)=0.3$ and $P(E \cup F)=0.5$,then $P(E|F)-P(F|E)$ equals

Two cards are drawn one by one from a pack of cards. The probability of getting the first card as an ace and the second as a coloured card is (without replacement).

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:

$A$ fair die is tossed until a six is obtained. Let $X$ be the number of required tosses,then the conditional probability $P(X \geq 5 \mid X > 2)$ is: