A bag contains $5$ black balls, $4$ white balls and $3$ red balls. If a ball is selected randomwise, the probability that it is a black or red ball is

Let $A$ denote the event that a $6 -$digit integer formed by $0,1,2,3,4,5,6$ without repetitions, be divisible by $3 .$ Then probability of event $A$ is equal to :

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$ roll than the number obtained in the $(i-1)^{\text {th }}$ roll, $i=2,3$, is equal to :

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is

If a party of $n$ persons sit at a round table, then the odds against two specified individuals sitting next to each other are

From a pack of playing cards three cards are drawn simultaneously. The probability that these are one king, one queen and one jack is