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.

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9 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4

1
$264$ $264$ people saw a play at a theatre. Each person went to the afternoon (matinee) performance or to the evening performance.
- The ratio of the number at the matinee to the number at the evening performance was $5 : 6$
- $53$ of the people at the evening performance bought a programme.
- Altogether, $98$ people bought a programme.
(a) Complete the frequency tree.(4 marks)
(b) One of the people who bought a programme is chosen at random.

Work out the probability that this person was at the matinee.

(1 mark)
Level 3 · 5 marksTry it
2
A florist sells bunches of roses and bunches of tulips. Some of the bunches are wrapped in paper.

In one week the florist sold $240$ bunches. $\frac{3}{8}$ of these bunches were roses.

The frequency tree shows some information about the bunches sold that week.(a) Work out the number of bunches of tulips sold that week.

(2 marks)
(b) Complete the frequency tree.

(2 marks)
(c) Show that more than a third of the bunches sold that week were wrapped in paper.

(2 marks)
Level 3 · 6 marksTry it
3
Priya plays one game of a word puzzle each day. For each game she notes whether she played in the morning or in the evening, and whether she won or lost.

Her results are shown in the frequency tree.(a) How many games did Priya play in the evening?

(1 mark)
(b) Use Priya's results to estimate the probability that she wins her next game.

(2 marks)
(c) Priya saysI am more likely to win when I play in the morning than when I play in the evening.Is Priya right?

Show how you decide.

$\ldots\ldots\ldots\ldots$ because $\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots$

(3 marks)
Level 3 · 6 marksTry it
4
A garage serviced $150$ cars last month. Each car was either petrol or electric.

The frequency tree shows how many of the cars needed new tyres.(a) One of the electric cars is chosen at random.

Write down the probability that it needed new tyres.

(1 mark)
(b) Work out the percentage of all the cars that needed new tyres.

(2 marks)
(c) Given that a car chosen at random needed new tyres, find the probability that it is electric.

(2 marks)
Level 3 · 5 marksTry it
5
A garden centre sold $320$ $320$ plants last week.
- The ratio of indoor plants sold to outdoor plants sold was $3 : 5$
- $25\%$ of the indoor plants were sold online.
- Altogether, $86$ of the plants were sold online.
(a) Complete the frequency tree.(4 marks)
(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

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