$A$ black and a red dice are rolled. Find the conditional probability of obtaining the sum $8$,given that the red die resulted in a number less than $4$.

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:

One ticket is selected at random from $100$ tickets numbered $00, 01, 02, \dots, 98, 99$. If $X$ and $Y$ denote the sum and the product of the digits on the tickets,then $P(X = 9 | Y = 0)$ equals

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

If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P(B \mid A) = 1$,then . . . . . . .

$A$ cubical die with faces marked $1, 2, 3, ..., 6$ is tossed such that the probability of throwing the number $t$ is proportional to $t^2$. The probability that the number $5$ has appeared,given that the number turned up is not even,is: