A group of $40$ students took a test in Economics. The following Venn diagram shows that $19$ boys $\left(\mathrm{B}\right)$ took the test and that seven students failed the test $\left(F\right)$

Describe the $21$ students who are members of the set $B^{\text{'}}$.

A group of $40$ students took a test in Economics. The following Venn diagram shows that $19$ boys $\left(\mathrm{B}\right)$ took the test and that seven students failed the test $\left(F\right)$

Find the probability that a randomly selected student is a boy or someone who failed the test.

The following table gives information about all the animals on a farm.

Find the probability that a randomly selected animal is:

male or a goat

The following table gives information about all the animals on a farm.

Find the probability that a randomly selected animal is:

a female or a sheep.

The following table gives information about all the animals on a farm.

a male or goat and a sheep or female.

Find a different way of describing each of the two types of animal.

Two ordinary fair dice are rolled and three events are:
$X:$ the sum of the two numbers rolled is $6 .$
$Y$ : the difference between the two numbers rolled is zero.
$Z$ : both of the numbers rolled are even.

List the outcomes that are favourable to:

$X$ and $Y$

Two ordinary fair dice are rolled and three events are:
$X:$ the sum of the two numbers rolled is $6 .$
$Y$ : the difference between the two numbers rolled is zero.
$Z$ : both of the numbers rolled are even.

List the outcomes that are favourable to:

$X$ and $Z$

Two ordinary fair dice are rolled and three events are:
$X:$ the sum of the two numbers rolled is $6 .$
$Y$ : the difference between the two numbers rolled is zero.
$Z$ : both of the numbers rolled are even.

List the outcomes that are favourable to:

$Y$ and $Z$

Two ordinary fair dice are rolled and three events are:
$X:$ the sum of the two numbers rolled is $6 .$
$Y$ : the difference between the two numbers rolled is zero.
$Z$ : both of the numbers rolled are even.

List the outcomes that are favourable to: $X \& Y, Y\& Z, Z \& X$

What do your answers tell you about the events $X, Y$ and $Z$ ?