When two dice are rolled,what is the probability that the sum of the numbers on the faces is a multiple of $4$?

$A$ problem in statistics is given to three students $A, B$ and $C$. Their probabilities of solving the problem are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. If all of them try independently,then the probability that the problem is solved is

If any four numbers are selected,what is the probability that the last digit of their product will be $1, 3, 5$ or $7$?

Two dice are thrown. If the first die shows $5$,what is the probability that the sum of the numbers on both dice is $8$ or more than $8$?

$A$ special lottery is to be held to select a student who will live in the only deluxe room available in a hostel. $100$ $III$ year,$150$ $II$ year,and $200$ $I$ year students have applied for the room. Each $III$ year student's name is placed in the lottery $3$ times,each $II$ year student's name $2$ times,and each $I$ year student's name $1$ time. The probability that a $III$ year student gets the room is:

In each of the following experiments,specify the appropriate sample space: $A$ boy has a $1$ rupee coin,a $2$ rupee coin,and a $5$ rupee coin in his pocket. He takes out two coins out of his pocket,one after the other.