The probabilities of $A$ and $B$ dying in a year are $p$ and $q$ respectively. What is the probability that only one of them will be alive at the end of the year?

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three persons apply for the same house is

The probability of a student qualifying for $IITJEE$ and $EAMCET$ are $\frac{1}{5}$ and $\frac{3}{5}$ respectively. The probability that the student qualifies for at least one of these tests is:

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

$A$ manager decides to distribute $Rs. 20000$ between two employees $X$ and $Y$. He knows $X$ deserves more than $Y$,but does not know how much more. So,he decides to arbitrarily break $Rs. 20000$ into two parts and gives $X$ the bigger part. Then,the chance that $X$ gets twice as much as $Y$ or more is

$A$ 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: