GCSE · Basic probability
Frequency treesExam-style questions
A frequency tree sorts one group by two questions, and every box is a count that splits into the boxes after it. How to complete a tree from facts in words (counts, fractions, percentages or a ratio), work backwards from a partly filled tree, turn it into a two-way table, and read off fractions and probabilities with the right group on the bottom.
9 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try
- 1A garden centre sold plants last week.
- The ratio of indoor plants sold to outdoor plants sold was
- of the indoor plants were sold online.
- Altogether, of the plants were sold online.
(b) One of the outdoor plants sold last week is chosen at random.
Work out the probability that it was sold online.
(2 marks)Level 4 · 6 marksTry it - 2A cycle shop sold bikes last year.
of the bikes sold were electric.
of the electric bikes were sold to people aged over
of the bikes that were not electric were sold to people aged over
(a) Use this information to complete the frequency tree.(3 marks)
Sam says,
“The people aged over who bought a bike were more likely to buy an electric bike than a bike that was not electric.”
(b) Is Sam correct?
You must show how you get your answer.
(2 marks)Level 4 · 5 marksTry it - 3people took part in a charity walk. Each person walked either the short route or the long route.
of the people walked the short route.
On the long route, twice as many people raised more than £ as did not.
Altogether, people raised more than £
(a) Complete the frequency tree.(4 marks)
(b) One of the people who raised more than £ is chosen at random.
Work out the probability that this person walked the long route.
(2 marks)Level 4 · 6 marksTry it - 4A college has students. Each student studies either A levels or a vocational course.
- of the students study A levels.
- of the students who study A levels have a part-time job.
- A student on a vocational course is twice as likely to have a part-time job as a student who studies A levels.
(4 marks)
(b) Complete the frequency tree.(2 marks)
(c) A student with a part-time job is chosen at random.
Find the probability that this student is on a vocational course.
(2 marks)Level 4 · 8 marksTry it - 5The frequency tree shows some information about the members of a choir. Each member is an adult or a child, and each member sings soprano or alto.A member of the choir is chosen at random.
The probability that this member is a child is
(a) Work out the number of members of the choir.
(3 marks)
(b) What fraction of the members who sing soprano are children?
(2 marks)Level 4 · 5 marksTry it