$A$ bag contains $8$ red and $7$ black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is

$A$ bag contains $6$ blue and $6$ green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is:

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

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:

If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3, 4, 5\}$ and $B=\{1, 2, 3, 4\}$ respectively, then the probability that the equation $x^2+ax+b=0$ has real roots is

$A$ bag contains $6$ white and $4$ black balls. $A$ die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is: