Probabilities from Venn Diagrams (Cambridge (CIE) IGCSE International Maths)

• Be careful when filling in numbers for a Venn diagram

  • Some of the given numbers may need to be split between two sections of the Venn diagram

• Suppose 10 people have a cat, 8 people have a dog and 6 people have both a cat and a dog

  • Out of the 10 people who have a cat

    • 6 also have a dog

    • 4 do not have a dog

  • Out of the 8 people who have a dog

    • 6 also have a cat

    • 2 do not have a cat

In a class of 30 students, 15 students study Spanish and 3 of the Spanish students also study German.
7 students study neither Spanish nor German.

(a) Draw a Venn diagram to show this information.

Draw the Venn diagram with its rectangular box and two (labelled) overlapping circles
3 students study both Spanish and German, so start here and work outwards
12 must study Spanish but not German (to get 15 in total for Spanish)
7 study neither, so this goes outside of the circles
To get 30 in total, 8 must study German but not Spanish

(b) Use your Venn diagram to find the probability that a student, selected at random from the class, studies Spanish but not German.

It helps to highlight Spanish but not German

Divide the number of students studying Spanish but not German by the total number of students

Students studying Spanish but not German = 12
Total number of students = 30

P(Spanish but not German)