Frequency Trees: Higher Tier Practice - Worksheets, Questions and Revision

4 original exam-style questions - 2 pages of questions with a full mark scheme - free printable PDF.

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3.19H Frequency Trees: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 75 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A school runs a trial of two revision methods, X and Y. 60% of students try method X and 40% try method Y. Of those using X, 70% improve their grade. Of those using Y, 50% improve.
Using a frequency tree starting with 1000 students, work out how many students improve after trying method Y, and how many students improve in total.
(a)Using 1000 students as the starting frequency, work out how many students improve after trying method Y.(2)
(b)Using the same 1000 students, work out the total number of students who improve (from both methods).(2)
(Total for Question 1 is 4 marks)
2
In a survey 300 people are asked whether they exercise regularly and whether they take a vitamin supplement. The frequency tree starts with 300 people: 60% exercise regularly. Of those who exercise, 30% take a supplement. Of those who do not exercise, 10% take a supplement.
Complete the frequency tree values and find the probability that a randomly chosen person both exercises regularly and takes a supplement. Give your answer as a fraction in lowest terms.
(a)Complete the frequencies on the tree (write the four end frequencies).(2)
(b)Write down the probability that a randomly chosen person both exercises regularly and takes a supplement, giving your answer as a fraction in lowest terms.(2)
(Total for Question 2 is 4 marks)
3
A medical trial tests a new treatment. Out of 200 patients, 40% receive the treatment and 60% receive a placebo. Of those receiving the treatment, 75% show improvement. Of those receiving placebo, 20% show improvement.
(a) Complete a frequency tree showing actual frequencies.
(b) Calculate the probability that a randomly chosen patient shows improvement.
(c) Given a patient shows improvement, calculate the probability they were in the treatment group. Give your answer as a fraction in lowest terms.
(a)(a) Complete the frequency tree with actual numbers.(1)
(b)(b) Calculate the probability that a randomly chosen patient shows improvement.(2)
(c)(c) Given a patient shows improvement, calculate the probability they were in the treatment group. Give your answer as a fraction in lowest terms.(2)
(Total for Question 3 is 5 marks)
4
A college runs morning and evening exam sessions. 20% of the 500 candidates sit the morning session and the rest sit in the evening. 60% of evening candidates pass. Let p be the proportion of morning candidates who pass. If the total number of passes is 290, work out p as a percentage.
(a)Set up an equation for the total number of passes in terms of p, then solve for p. Give p as a percentage to the nearest whole percent.(4)
(Total for Question 4 is 4 marks)
Mark scheme · 3.19H Frequency Trees: Higher Tier Practice

Question 1

Question 2

Question 3

Question 4