$A$ box contains $5$ red marbles,$8$ white marbles and $4$ green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be
$(i)$ red?
$(ii)$ white?
$(iii)$ not green?

Which of the following arguments are correct and which are not correct? Give reasons for your answer.
$(i)$ If two coins are tossed simultaneously,there are three possible outcomes - two heads,two tails,or one of each. Therefore,for each of these outcomes,the probability is $\frac{1}{3}$.
$(ii)$ If a die is thrown,there are two possible outcomes - an odd number or an even number. Therefore,the probability of getting an odd number is $\frac{1}{2}$.

$A$ bag contains a red ball,a blue ball and a yellow ball,all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the
$(i)$ yellow ball?
$(ii)$ red ball?
$(iii)$ blue ball?

$A$ die is thrown once. Find the probability of getting:
$(i)$ a prime number;
$(ii)$ a number lying between $2$ and $6$;
$(iii)$ an odd number.

$A$ jar contains $24$ marbles,some are green and others are blue. If a marble is drawn at random from the jar,the probability that it is green is $\frac{2}{3}$. Find the number of blue balls in the jar.

It is given that in a group of $3$ students,the probability of $2$ students not having the same birthday is $0.992$. What is the probability that the $2$ students have the same birthday?