If $5$ distinct balls are placed at random into $5$ cells, then the probability that exactly one cell remains empty is (in $/ 125$)

The corners of regular tetrahedrons are numbered $1, 2, 3, 4$. Three tetrahedrons are tossed. The probability that the sum of the upward corners will be $5$ is

$A$ and $B$ are two candidates seeking admission in a college. The probability that $A$ is selected is $0.7$ and the probability that exactly one of them is selected is $0.6$. Find the probability that $B$ is selected.

Two natural numbers are chosen at random from $1$ to $100$ and are multiplied. If $A$ is the event that the product is an even number and $B$ is the event that the product is divisible by $4$,then $P(A \cap \bar{B})=$

The probability that the product of the outcomes when three dice are rolled simultaneously is divisible by $4$ is equal to

$P$ speaks truth in $70\%$ of the cases and $Q$ in $80\%$ of the cases. In what percent of cases are they likely to agree in stating the same fact (in $\%$)?