Two children are selected from a group in which there are $10$ more boys than girls. Given that there are $756$ equiprobable ordered selections that can occur, find the probability that two boys or two girls are selected.    [correct up to three decimal places]

Four quality-control officers were asked to test $1214$ randomly selected electronic components from a company's production line, and to report the proportions that they found to be defective. The proportions reported were:
$\frac{2}{333}, \frac{3}{411}, \frac{0}{187}$ and $\frac{4}{283}$.

These figures confirm what the manager thought; that about $k\%$ of the components produced are defective. Of the $7150$ components that will be produced next month, approximately how many does the manager expect to be defective?

The diagram opposite gives details about a company's $115$ employees. For example, it employs four unqualified, part-time females.

Two employees are selected at random. Find the probability that:

one is a qualified male and the other is an unqualified female

The diagram opposite gives details about a company's $115$ employees. For example, it employs four unqualified, part-time females.

Two employees are selected at random. Find the probability that:

both are unqualified, given that neither is employed part-time.

The numbers of books read in the past $3$ months by the members of a reading club are shown in the following table.

Find the probability that three randomly selected members have all read fewer than eight books, given that they have all read more than four books.