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.

One hundred people are attending a conference. The following Venn diagram shows how many are male $\left(M\right)$, have brown eyes $\left(BE\right)$ and are right-handed $\left(RH\right)$.

Given that there are $43$ males with brown eyes, $42$ right-handed males and 46 right-handed people with brown eyes, copy and complete the Venn diagram.

One hundred people are attending a conference. The following Venn diagram shows how many are male $\left(M\right)$, have brown eyes $\left(BE\right)$ and are right-handed $\left(RH\right)$.

Two attendees are selected at random. Find the probability that they are both females who are not right-handed.       [correct up to five decimal places]

One hundred people are attending a conference. The following Venn diagram shows how many are male $\left(M\right)$, have brown eyes $\left(BE\right)$ and are right-handed $\left(RH\right)$.

Two attendees are selected at random. Find the probability that exactly one of them is right-handed, given that neither of them have brown eyes.      [correct up to three decimal places]