Of a group of five students, two will be selected for a school trip by picking names out of a hat. The five students are Jack, Mary, Rafa, Harry and Pietronella.

With the aid of a tree diagram or a table of outcomes, find the number of different possible combinations of students that could be selected.

Of a group of five students, two will be selected for a school trip by picking names out of a hat. The five students are Jack, Mary, Rafa, Harry and Pietronella.

Find the probability that Mary and Pietronella will go on the trip.

Alix has a box of red, yellow and green marbles. She picks a marble from the box, without looking.
The table shows the probabilities of picking the different colors.

$\begin{array}{|cc|}\hline \text{ Color }& \text{ Probability }\\ \text{ red }& 0.4\\ \text{ yellow }& 0.25\\ \text{ green }& \\ \hline\end{array}$

What is the probability that Alix picks a green marble? 

Alix has a box of red, yellow and green marbles. She picks a marble from the box, without looking.
The table shows the probabilities of picking the different colors.

$\begin{array}{|cc|}\hline \text{ Color }& \text{ Probability }\\ \text{ red }& 0.4\\ \text{ yellow }& 0.25\\ \text{ green }& \\ \hline\end{array}$

There are $5$ yellow marbles in the box. How many red marbles are there?

Alix has a box of red, yellow and green marbles. She picks a marble from the box, without looking.
The table shows the probabilities of picking the different colors.

$\begin{array}{|cc|}\hline \text{ Color }& \text{ Probability }\\ \text{ red }& 0.4\\ \text{ yellow }& 0.25\\ \text{ green }& \\ \hline\end{array}$

Alix picks a marble, then replaces it in the box and picks another.

Draw a tree diagram to show the probabilities.

Alix has a box of red, yellow and green marbles. She picks a marble from the box, without looking.
The table shows the probabilities of picking the different colors.

$\begin{array}{|cc|}\hline \text{ Color }& \text{ Probability }\\ \text{ red }& 0.4\\ \text{ yellow }& 0.25\\ \text{ green }& \\ \hline\end{array}$

Alix picks a marble, then replaces it in the box and picks another.

What is the probability that at least one of the marbles is red?

In a group of $40$ people, $35$ choose a main course, $10$ choose a starter and $7$ choose both.
Draw a Venn diagram to represent this information.

In a group of $40$ people, $35$ choose a main course, $10$ choose a starter and $7$ choose both. What is the probability that a person picked at random chooses a main course but no starter?

A group of $30$ children are asked if they play lacrosse$\left(L\right)$, basketball$\left(B\right)$, volleyball$\left(V\right)$ or none of these sports. The results are:

$3$ children do not play any of these sports, $2$ children play all three sports, $6$ play volleyball and basketball, $3$ play lacrosse and basketball,  $6$ play lacrosse and volleyball,
$16$ play basketball, $12$ play volleyball.

Draw a Venn diagram to display this information.