$A$ bag contains $8$ black and $7$ white balls. Two balls are drawn at random. For which outcome is the probability the highest?

Three squares of a chessboard are selected at random. The probability of selecting two squares of one colour and the other of a different colour is equal to

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. $A$ fair die is thrown three times. If $r_1, r_2,$ and $r_3$ are the numbers obtained on the die,what is the probability that $\omega^{r_1} + \omega^{r_2} + \omega^{r_3} = 0$?

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 two numbers $a$ and $b$ are chosen from the first $30$ natural numbers,what is the probability that $a^2 - b^2$ is divisible by $3$?

Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively?