# StudySquare

# SQA Higher Maths Tree and Venn diagrams

This page covers the following topics:

One way of showing combinations of multiple events is through tree diagrams. Each branch is labelled at the end with its outcome and the probability is written alongside the line.

Venn diagrams use circles to represent sets of outcomes. They can show intersections of outcomes (i.e. where both outcomes happen) and unions (the probability of either or both outcomes occuring).

# 1

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Tiles with the following letters are placed in a bag: BANANA. A tile is taken, the letter recorded, and then replaced before a second tile is drawn. Calculate the probability that neither of the tiles are the letter A (hint: use a tree diagram).

# 2

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There are 30 people on a plane. 15 of these are British, 10 are Spanish and the remainder are American. Use a tree diagram to calculate the probability that neither of the first 2 people who get off the plane are British.

# 3

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There are 48 dogs in a kennels. 1/6 of the dogs are completely white, 1/6 are completely black and 1/6 are completely brown. 1/8 of the dogs have brown and white markings, 1/8 have black and brown, 1/8 have black and white and the final 1/8 have all 3. Draw a Venn diagram to represent the colours of the dogs in the kennels.

# 4

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20 children in a school are asked which subjects they enjoyed. 6 said they enjoyed maths, 10 said they enjoyed english and 4 said they enjoyed art. 1 of these children said they enjoyed all 3 subjects and 3 enjoyed both maths and english. 0 enjoyed both maths and art or english and art. Sketch a Venn diagram to represent this information.

# 5

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A restaurant conducts a survey to see their customers favourite dishes on the menu. They represent the results on a Venn diagram. The results were as followed: 12 pizza, 34 pasta, 16 salad. Of these, 4 voted all 3, 7 voted both pizza and pasta (without salad) and 2 voted both pasta and salad (without pizza). None voted pizza and salad without pasta. How many people took part in the survey?

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