Let $A$ be a set containing $n$ elements. If $P$ and $Q$ are two subsets of $A$,then the number of ways of choosing $P$ and $Q$ such that $P \cap Q = \phi$ is:

In a certain town,$65\%$ of families own cell phones,$15000$ families own scooters,and $15\%$ of families own both. Given that every family owns at least one of the two,the total number of families in the town is:

If $U$ is the universal set with $100$ elements; $A$ and $B$ are two sets such that $n(A)=50$,$n(B)=60$,and $n(A \cap B)=20$,then find $n(A^{\prime} \cap B^{\prime})$.

In a town of $10,000$ families,it was found that $40\%$ of families buy newspaper $A$,$20\%$ buy newspaper $B$,and $10\%$ buy newspaper $C$. Also,$5\%$ of families buy $A$ and $B$,$3\%$ buy $B$ and $C$,and $4\%$ buy $A$ and $C$. If $2\%$ of families buy all three newspapers,then the number of families that buy newspaper $A$ only is:

$A$ certain $12$-hour digital clock displays the hour and the minute of a day. Due to a defect in the clock,whenever the digit $1$ is supposed to be displayed,it displays $7$. What fraction of the day will the clock show the correct time?

In a city,$20\%$ of persons read an English newspaper,$40\%$ read a Hindi newspaper,and $5\%$ read both newspapers. The percentage of people who do not read either paper is: (in $\%$)