When two dice are thrown simultaneously,what is the probability that the sum of the numbers on the top faces is $5$?

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 $1$.

The probabilities of a problem being solved by two students are $\frac{1}{2}$ and $\frac{1}{3}$. Then the probability of the problem being solved is

Two dice are thrown simultaneously. The probability of obtaining a total score of $5$ is

$A$ die is thrown. Find the probability of the following event: $A$ number less than $6$ will appear.

If two dice are thrown simultaneously,then the probability that the sum of the numbers which come up on the dice is more than $5$ is: