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 $c$.

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.

An employee is randomly selected. Find:

$\mathrm{P}(M\mid FT)$

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.

An employee is randomly selected. Find:

$\mathrm{P}\left(FT\mid M^{\text{'}}\right)$

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.

An employee is randomly selected. Find:

$\mathrm{P}\left[\right(M\cap FT)\mid (M\cup FT\left)\right]$.

The circular archery target shown, on which $1, 2, 3$ or $5$ points can be scored, is divided into four parts of unequal area by concentric circles. The radii of the circles are $3 \mathrm{cm}, 9 \mathrm{cm}, 15 \mathrm{cm}$ and $30 \mathrm{cm}$.

You may assume that a randomly fired arrow pierces just one of the four areas and is equally likely to pierce any part of the target.

Show that the probability of scoring $5$ points is $0.01$.

The circular archery target shown, on which $1, 2, 3$ or $5$ points can be scored, is divided into four parts of unequal area by concentric circles. The radii of the circles are $3 \mathrm{cm}, 9 \mathrm{cm}, 15 \mathrm{cm}$ and $30 \mathrm{cm}$.

You may assume that a randomly fired arrow pierces just one of the four areas and is equally likely to pierce any part of the target.

Find the probability of scoring $3$ points, $2$ points and $1$ point with an arrow.