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

The probability that $A$ speaks truth is $75 \%$ and the probability that $B$ speaks truth is $80 \%$. The probability that they contradict each other when asked to speak on a fact is

If $A$ and $B$ are two events,then the probability of the event that at most one of $A$ and $B$ occurs is:

$A$ speaks truth in $75 \%$ of the cases and $B$ in $80 \%$ of the cases. Then,the probability that their statements about an incident do not match,is

If a man throws a die until he gets a number bigger than $3$,then the probability that he gets a $5$ in his last throw is

For three events $A$, $B$, and $C$ of a sample space, $P(\text{exactly one of } A \text{ or } B \text{ occurs}) = P(\text{exactly one of } B \text{ or } C \text{ occurs}) = P(\text{exactly one of } C \text{ or } A \text{ occurs}) = \frac{1}{4}$. If the probability of all the three events occurring simultaneously is $\frac{1}{16}$, then the probability that at least one of the events occurs is: