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 $NCC$.

$A$ student appears for tests $I$,$II$,and $III$. The student is successful if they pass in tests ($I$ and $II$) $OR$ ($I$ and $III$). The probabilities of the student passing in tests $I$,$II$,and $III$ are respectively $p$,$q$,and $1/2$. If the probability of the student being successful is $1/2$,then:

The probability that a teacher will give an unannounced test during any class meeting is $1/5$. If a student is absent twice,then the probability that the student will miss at least one test is

$A, B, C, D$ cut a pack of $52$ well-shuffled playing cards successively in the same order. If the person who cuts a spade first wins the game and the game continues until this happens,then the probability that $A$ wins the game is

If $A$ and $B$ are events such that $P(A \cup B) = 3/4,$ $P(A \cap B) = 1/4,$ and $P(\bar{A}) = 2/3,$ then $P(\bar{A} \cap B)$ is

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