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:

If $A$ and $B$ are mutually exclusive events with $P(A)=\frac{1}{4}$ and $P(B)=\frac{3}{7}$,then what is the value of $P(A / A \cup B)$?

Two dice are thrown together. If the numbers appearing on the two dice are different,then what is the probability that the sum is $6$?

Two fair dice are thrown simultaneously. The probability of getting the same number on both dice is $......$.

The probability that an ordinary or a non-leap year has $53$ Sundays is

$A$ 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: