In a box there are $8$ red,$7$ blue,and $6$ green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

The probabilities of a student getting $I, II$ and $III$ division in an examination are respectively $\frac{1}{10}, \frac{3}{5}$ and $\frac{1}{4}$. The probability that the student fails in the examination is

$A$ fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is $3$.

The probability for a contractor to get a road contract is $\frac{2}{9}$ and to get a building contract is $\frac{5}{9}$. If the probability to get both the contracts is $\frac{1}{6}$,then what is the probability to get neither of these two contracts?

Let $A$ and $B$ be events for which $P(A) = x$,$P(B) = y$,and $P(A \cap B) = z$. Then $P(\bar{A} \cap B)$ equals:

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?