If a $3$-digit number is randomly chosen,what is the probability that either the number itself or some permutation of the number (which is a $3$-digit number) is divisible by $4$ and $5$?

If $A$ and $B$ are two independent events such that $P(A) > 0.5$,$P(B) > 0.5$,$P(A \cap \bar{B}) = \frac{3}{25}$,and $P(\bar{A} \cap B) = \frac{8}{25}$,then $P(A \cap B)$ is:

Four persons $A$, $B$, $C$ and $D$ throw an unbiased die, turn by turn, in succession till one gets an even number and wins the game. What is the probability that $A$ wins if $A$ begins?

There are $3$ bags $A, B$ & $C$. Bag $A$ contains $1$ Red & $2$ Green balls,bag $B$ contains $2$ Red & $1$ Green balls and bag $C$ contains only $1$ Green ball. One ball is drawn from bag $A$ & put into bag $B$,then one ball is drawn from $B$ & put into bag $C$,& finally one ball is drawn from bag $C$ & put into bag $A$. When this operation is completed,what is the probability that bag $A$ contains $2$ Red & $1$ Green balls?

There are $3$ houses available in a residential area. $3$ people apply for the houses. If each person applies for a house without consulting others,what is the probability that all $3$ apply for the same house (in $/9$)?

The probability of occurrence of an event is $\frac{2}{5}$ and the probability of non-occurrence of another event is $\frac{3}{10}$. If these events are independent,then the probability that only one of the two events occur is