Dean Chalmers and Julian Gilbey Solutions for Chapter: Probability, Exercise 7: EXERCISE 4E

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.

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:

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

Two fair triangular spinners, both with sides marked $1, 2$ and $3$, are spun. Given that the sum of the two numbers spun is even, find the probability that the two numbers are the same.

Two ordinary fair dice are rolled and the two numbers rolled are added together to give the score. Given that a player's score is greater than $6$ , find the probability that it is not greater than $8$

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.

Given that an arrow does not score $5$ points, find the probability that it scores $1$ point.

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.

Given that a total score of $6$ points is obtained with two randomly fired arrows, find the probability that neither arrow scores $1$ point.