Venn Diagrams

A Venn diagram displays information using overlapping circles. The area of overlap means that the item fits into both categories.

For example, in Class 10A:

  • 10 children like oranges
  • 5 children like both oranges and apples
  • 12 children only like apples
  • 3 children don’t like either oranges or apples

Let’s represent this information in a Venn Diagram:

Practice Questions

Question 1:

How many children are there in the class in total?

To solve this, we must add up all the different sections together:

5 (only like oranges) + 5 (like both) + 12 (only like apples) + 3 (like neither) = 25 children


Question 2:

How many children like apples?

To find this answer, we must consider two sections—the children who like only apples, and the children who like both apples and oranges.

Add these two together:

5 + 12 = 175 + 12 = 17 children like apples


Question 3:

A child is chosen at random from the class. What is the probability that they like apples?

Write down both the total number of children in the class, and the number of children who like apples:

  • Total number of children in the class = 25
  • Number of children who like apples = 17

Write this as a fraction:

\frac{17}{25}\frac{17}{25}


Question 4:

A child is chosen at random from the class. What is the probability that they don’t like oranges?

Write down both the total number of children in the class, and the number of children who don’t like oranges:

  • Total number of children in the class = 25
  • Number of children who don’t like oranges = 12 (only like apples) + 3 (don’t like either fruit) = 15

Write this as a fraction:

\frac{15}{25}\frac{15}{25}

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