[discia] GCSE Maths › Probability › Frequency Trees

Frequency Trees

discia.org 10 questions · 47 marks
Name Date
  1. Either paper 5 marks

    38 students took a mock exam. The frequency tree shows some information about the results.

    38Boys 13Girls ?Passed 8Failed ?Passed ?Failed ?

    Altogether 25 of the students passed.

    (a)

    Complete the frequency tree.

    (b)

    One of the 38 students is chosen at random.

    Work out the probability that the student is a girl who passed.

    Show answer
    (a) Girls 25, boys who failed 5, girls who passed 17, girls who failed 8
    (b) \(\frac{17}{38}\)
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  2. Either paper 4 marks

    33 students were asked how they travelled to school one morning and whether they were late. The frequency tree shows the results.

    33Bus 15Walk 18Late 4On time 11Late 4On time 14
    (a)

    One of these students is chosen at random.

    Calculate the probability that the student walked and was late.

    (b)

    One of the students who came by bus is chosen at random.

    Calculate the probability that this student was late.

    Show answer
    (a) \(\frac{4}{33}\)
    (b) \(\frac{4}{15}\)
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  3. Either paper 4 marks

    79 members pay to use a gym.

    They all have the standard membership for \(£22\) per month.

    Some also have the swimming pool pass for \(£17\) extra per month.

    Some also have the fitness classes pass for \(£4\) extra per month.

    The frequency tree shows the number of members with each package.

    79Pool 37No pool 42Classes 16No classes21Classes 22No classes20

    In total, how much per month do the 79 members pay?

    Show answer
    \(\text{£}2519\)
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  4. Either paper 3 marks

    A walking group has 52 members. One week it ran a Wednesday walk and a Saturday walk.

    The frequency tree shows some information about the members who went on the walks.

    52Wednesday ?NotWednesday 37Saturday 8Not Saturday?Saturday ?Not Saturday?

    27 members went on the Saturday walk.

    The Venn diagram is to show the same information. The number who went on both walks has been filled in from the tree. The other regions are labelled P, Q and R.

    \(\xi\) = the 52 members, \(W\) = members who went on the Wednesday walk, \(S\) = members who went on the Saturday walk.

    WSR8QξP
    (a)

    Work out the number of members in region P.

    (b)

    Work out the number of members in region Q.

    (c)

    Work out the number of members in region R.

    Show answer
    (a) \(18\)
    (b) \(19\)
    (c) \(7\)
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  5. Either paper 5 marks

    54 people were asked how they got to work one morning and whether they arrived late. The frequency tree shows some of the results.

    54Car 19Train 18Walk ?Late 7On time ?Late 3On time ?Late ?On time 11

    Altogether 16 of them arrived late.

    (a)

    Complete the frequency tree.

    (b)

    One of the 54 people is chosen at random.

    Work out the probability that this person went by train and was on time.

    Show answer
    (a) Walk 17, car and on time 12, train and on time 15, walk and late 6
    (b) \(\frac{5}{18}\)
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  6. Either paper 5 marks

    A group of members were asked whether they had renewed.

    \(200\) members were asked altogether.

    200Adults ?Juniors ?Renewed ?Not renewed?Renewed 79Not renewed?

    \(40\%\) of the members were adults.

    \(80\%\) of the adults had renewed.

    (a)

    Work out how many of the members were juniors.

    (b)

    Work out how many of the adults had renewed.

    (c)

    One of the \(200\) members is chosen at random.

    Calculate the probability that this person had renewed.

    Show answer
    (a) \(120\ \text{members}\)
    (b) \(64\)
    (c) \(\frac{143}{200}\)
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  7. Either paper 5 marks
    \(245\) students from Year 10 and Year 11 take part in a competition. 245Year 10 ?Year 11 ?Medal ?No medal ?Medal ?No medal ?
    • There are \(147\) more Year 10 students than Year 11 students.
    • \(53\) of the students win a medal.
    • \(12\) of the students who win a medal are in Year 11.
    (a)

    Calculate the number of Year 10 students.

    (b)

    Use your answer to part (a) to complete the frequency tree.

    Show answer
    (a) \(196\ \text{students}\)
    (b) Year 10 196: Medal 41, No medal 155. Year 11 49: Medal 12, No medal 37
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  8. Either paper Higher6 marks

    19 men and 47 women use a leisure centre. 16 of these people use the pool.

    Four times as many women as men do not use the pool.

    66Men 19Women 47Pool ?No pool ?Pool ?No pool ?
    (a)

    Complete the frequency tree.

    (b)

    One of the people who use the pool is chosen at random.

    Calculate the probability that this person is a man.

    Give your answer as a fraction in its simplest form.

    Show answer
    (a) Men: Pool 9, No pool 10. Women: Pool 7, No pool 40
    (b) \(\frac{9}{16}\)
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  9. Either paper 5 marks

    Some visitors arrive by train or by car.

    Branch A is the visitors who came by train, and branch B is the visitors who came by car.

    ?A ?B ?Booked 3Not booked37Booked ?Not booked ?

    The number of visitors who came by car is \(3\) times the number who came by train.

    \(\frac{1}{ 3 }\) of the visitors who came by car booked in advance.

    (a)

    Calculate how many visitors came by train.

    (b)

    Calculate how many visitors there were altogether.

    (c)

    Find the probability that a randomly chosen visitor booked in advance.

    Give your answer as a fraction in its simplest form.

    Show answer
    (a) \(40\ \text{visitors}\)
    (b) \(160\ \text{visitors}\)
    (c) \(\frac{43}{160}\)
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  10. Either paper 5 marks

    34 students took a mock exam. The frequency tree shows some information about the results.

    34Boys 18Girls ?Passed 10Failed ?Passed ?Failed ?

    Altogether 21 of the students passed.

    (a)

    Complete the frequency tree.

    (b)

    One of the 34 students is chosen at random.

    Calculate the probability that the student is a girl who passed.

    Show answer
    (a) Girls 16, boys who failed 8, girls who passed 11, girls who failed 5
    (b) \(\frac{11}{34}\)
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discia.org Frequency Trees · sheet 1
Answers Frequency Trees · sheet 1
  1. (a) Girls 25, boys who failed 5, girls who passed 17, girls who failed 8
    (b) \(\frac{17}{38}\)
  2. (a) \(\frac{4}{33}\)
    (b) \(\frac{4}{15}\)
  3. \(\text{£}2519\)
  4. (a) \(18\)
    (b) \(19\)
    (c) \(7\)
  5. (a) Walk 17, car and on time 12, train and on time 15, walk and late 6
    (b) \(\frac{5}{18}\)
  6. (a) \(120\ \text{members}\)
    (b) \(64\)
    (c) \(\frac{143}{200}\)
  7. (a) \(196\ \text{students}\)
    (b) Year 10 196: Medal 41, No medal 155. Year 11 49: Medal 12, No medal 37
  8. (a) Men: Pool 9, No pool 10. Women: Pool 7, No pool 40
    (b) \(\frac{9}{16}\)
  9. (a) \(40\ \text{visitors}\)
    (b) \(160\ \text{visitors}\)
    (c) \(\frac{43}{160}\)
  10. (a) Girls 16, boys who failed 8, girls who passed 11, girls who failed 5
    (b) \(\frac{11}{34}\)
discia.org Frequency Trees · sheet 1