The Venn diagram opposite shows the responses of $40$ girls who were asked if they have an interest in a career in nursing $\left(N\right)$, dentistry $\left(D\right)$ or human rights $\left(H\right)$.

Describe any group of girls for whom dentistry is the least popular career of interest.

The quiz marks of $40$ students are represented in the following bar chart.

Two students are selected at random from the group. Find the probability that the second student scored more than $5$ , given that the first student did not score more than $5$.

The quiz marks of $40$ students are represented in the following bar chart.

Two students are selected at random from the group. Find the probability that the second student:

scored more than $7$ , given that the first student scored more than $7$ .

The histogram shown represents the times taken, in minutes, for $115$ men to complete a task. Two men are selected at random from the group. Find the probability that the:

first man took less than $1$ minute, given that he took less than $3$ minutes

The histogram shown represents the times taken, in minutes, for $115$ men to complete a task. Two men are selected at random from the group. Find the probability that the:

second man took less than $6$ minutes, given that the first man took less than $1$ minute.

At an insurance company, $60\%$ of the staff are male $\left(M\right)$ and $70\%$ work full-time $\left(FT\right)$. The following Venn diagram shows this and one other piece of information.

What information is given by the value $0.10$ in the Venn diagram?

At an insurance company, $60\%$ of the staff are male $\left(M\right)$ and $70\%$ work full-time $\left(FT\right)$. The following Venn diagram shows this and one other piece of information.

Find the value of $a$, $b$ and $c$.