In a class of $60$ students,$30$ opted for $NCC$,$32$ opted for $NSS$,and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,find the probability that the student has opted for $NSS$ but not $NCC$.

Let $A, B$ and $C$ be three events associated with sample space $S$. $A, B$ and $C$ are pairwise independent and $P(A)=P(B)=P(C)=P$. If all of them cannot occur simultaneously,then $P(A \cup B \cup C)$ is equal to

$A$ box contains $6$ red marbles numbered from $1$ through $6$ and $4$ white marbles numbered $12$ through $15$. Find the probability that a marble drawn at random is white and odd-numbered.

The probability of an impossible event,i.e.,$P(\phi)$,is

If two fair dice are rolled,then the probability that the sum of the numbers on the upper faces is at least $9$,is

Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{\text{st}}$ die is less than the number appeared on the $2^{\text{nd}}$ die,$B$ be the event that the number appeared on the $1^{\text{st}}$ die is even and that on the $2^{\text{nd}}$ die is odd,and $C$ be the event that the number appeared on the $1^{\text{st}}$ die is odd and that on the $2^{\text{nd}}$ die is even. Then