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.

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.

Calculate the probability (in the least form of a ratio) that a child selected at random:  plays volleyball and basketball but not lacrosse.

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.

Calculate the probability (in the least form a ratio) that a child selected at random:  plays only lacrosse.

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.

Calculate the probability that a child selected at random:  plays only volleyball.

A group of $90$ students filled in a questionnaire about their free-time activities. The three most popular choices were: go to the cinema $\left(C\right)$, read $\left(R\right)$ and watch television $\left(T\right)$. The results were:

$26$ students watch television, read and go to the cinema
$20$ students watch television and go to the cinema only
$18$ students read and go to the cinema only
$10$ students read and watch television only
$60$ students watch television, $60$ students read, $70$ students go to the cinema.
Draw a Venn diagram to display this information.