When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other is

$A$ 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 $\frac{1}{5}$. What is the probability that only one of them will be selected?

$A$ game consists of tossing a coin $3$ times and noting its outcome. $A$ boy wins the game if all tosses give the same outcome (i.e.,three heads or three tails) and loses the game otherwise. The probability that the boy loses the game is

Two dice are thrown and the sum of the numbers appeared on the dice is noted. If $A$ is the event of getting a prime number as their sum and $B$ is the event of getting a number greater than $8$ as their sum,then $P(A \cap \overline{B})=$

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

$A$ container holds two balls. Both balls are black. If one white ball is added to the container and then one ball is drawn at random from the container,what is the probability that it is white?