The probability of obtaining a sum of $8$ in a single throw of two dice is:

Out of $100$ students,two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students,what is the probability that you both enter different sections?

$A$ box contains $1$ red and $3$ identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

In a set of $30$ game cards,$17$ are white and the rest are green. Out of $30$,$4$ white and $5$ green cards are marked $IMPORTANT$. If a card is chosen randomly from this set,then the probability of choosing a green card or an $IMPORTANT$ card is:

When two dice are thrown simultaneously,find the probability of the following:
$(1)$ The numbers are the same.
$(2)$ The difference between the numbers is $1$.

$4$-digit numbers are formed using the digits $4, 5, 6, 7, 8, 9$ allowing repetition of the given digits. If a number is chosen at random from those numbers thus formed, then the probability that it is exactly divisible by $3$ is