If $A$ and $B$ are two events,what is the probability that exactly one of them occurs?

$A$ coin is tossed. If the outcome is a head,a die is thrown. If the die shows up an even number,the die is thrown again. What is the sample space for the experiment?

In the following experiment,specify the appropriate sample space: $A$ person is noting down the number of accidents along a busy highway during a year.

If $X_1, X_2, \ldots, X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$ for $r = 1, 2, \ldots, n$,then the probability that none of the $n$ events occur is

When a die is thrown,let event $A$ be getting a number greater than $3$,and let event $B$ be getting a number less than $5$. What is $P(A \cup B)$?

$A$ man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. If they appear for the interview independently,then the probability that only one of them is selected is: