The coefficients $a, b, c$ in the quadratic equation $ax^2 + bx + c = 0$ are chosen from the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$. The probability of this equation having repeated roots is:

From $80$ cards numbered $1$ to $80$,two cards are selected randomly. The probability that both the cards have numbers divisible by $4$ is given by

If $4$ cards are selected from a deck of $52$ cards,what is the probability that all cards are of the suit 'hearts'?

$A$ bag contains $6$ white and $4$ black balls. Two balls are drawn at random. The probability that they are of the same colour is . . . . . .

Two different families $A$ and $B$ are blessed with an equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of family $B$ is $\frac{1}{12}$,then the number of children in each family is?

If $3$ dice are thrown, the probability of getting $10$ as the sum of the three numbers that appeared on the top faces of the dice is