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 $c$.

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:

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