An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is

In a consignment of $15$ articles,it is found that $3$ are defective. If a sample of $5$ articles is chosen at random from it,then the probability of having $2$ defective articles is

$A$ bag contains $a$ white and $b$ black balls. Two players $A$ and $B$ alternately draw a ball from the bag,replacing the ball each time after the draw,until one of them draws a white ball and wins the game. $A$ begins the game. If the probability of $A$ winning the game is three times that of $B$,then the ratio $a : b$ is

$A$ container contains nine balls: three red,four blue,and two green. If three balls are selected at random from the container without replacement,what is the probability that all three balls are of different colors?

$A$ dice is rolled three times. The probability of getting a larger number than the previous number each time is:

If each of the coefficients $a, b, c$ in the equation $ax^2 + bx + c = 0$ is determined by throwing a die,then the probability that the equation will have equal roots is: