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

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:

In a lottery,there are $90$ tickets numbered $1$ to $90$. If $5$ tickets are chosen at random,what is the probability that $2$ of the chosen tickets are $15$ and $89$?

There are $10$ engineering colleges and five students $A, B, C, D, E$. Each of these students received an offer from all of these $10$ engineering colleges. They randomly choose a college independently of each other. The probability that all get admission in different colleges can be expressed as $\frac{a}{b}$,where $a$ and $b$ are co-prime numbers. Then the value of $a + b$ is:

From a group of $10$ men and $5$ women,a four-member committee is to be formed such that it must contain at least one woman. The probability that the committee has more women than men 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?