Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 4: Practice 1

Here is a standard set of dominos.

One domino is selected at random. It is then replaced and a second domino is drawn at random. If $S$ is the set of outcomes of selecting $2$ dominos, write down $n\left(S\right)$.

Here is a standard set of dominos.

One domino is selected at random. It is then replaced and a second domino is drawn at random. If $S$ is the set of outcomes of selecting $2$ dominos, write down $n\left(S\right)$. Let $A$ be the event 'at least one of the values on the first domino is a six' and $B$ be the event 'the second domino is a double' (both values are the same). Explain whether or not these events are independent.

Here is a standard set of dominos.

One domino is selected at random. It is then replaced and a second domino is drawn at random. If $S$ is the set of outcomes of selecting $2$ dominos, write down $n\left(S\right)$. Let $A$ be the event 'at least one of the values on the first domino is a six' and $B$ be the event 'the second domino is a double' (both values are the same). Explain whether or not these events are independent. Verify your answer using the multiplication rule.

In a different class, four students take Mathematics only, two take both Mathematics and Science, six take Science only and $12$ take neither subject. Determine whether the choice of taking Mathematics and taking Science ar independent events for this class.

Students in an after-school activity programme register for either trampolining or table tennis. The table shows students' choices by gender:

A student is selected at random from the group. Find: $\mathrm{P}\text{ (male trampoliner) }$

Students in an after-school activity programme register for either trampolining or table tennis. The table shows students' choices by gender:

A student is selected at random from the group. Find: $\mathrm{P}\text{ (trampoliner) }$

Students in an after-school activity programme register for either trampolining or table tennis. The table shows students' choices by gender:

A student is selected at random from the group. Find: $\mathrm{P}\text{ (female) }$

Students in an after-school activity programme register for either trampolining or table tennis. The table shows students' choices by gender:

A student is selected at random from the group. Determine whether or not the events trampolining and table tennis are independent events.