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A table shows the marks obtained by pupils and the corresponding number of pupils for each mark. a) How many people are in the class? b) What is the probability of a pupil who scored 10 marks? c) What

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6 parts
a

34\text{34}

b

517\frac{5}{17}

c(i)

534\frac{5}{34}

c(ii)

1134\frac{11}{34}

c(iii)

2134\frac{21}{34}

c(iv)

534\frac{5}{34}

Step-by-step solution

15 steps

Here is the solution based on the provided image.

The table shows the marks obtained by pupils and the corresponding number of pupils for each mark.

The table is:

MARKS INNumber of pupils11111010114488\begin{array}{|c|c|} \hline \text{MARKS IN} & \text{Number of pupils} \\ \hline 11 & 11 \\ 10 & 10 \\ 1 & 1 \\ 4 & 4 \\ 8 & 8 \\ \hline \end{array}

Part a· 1 step

How many people are in the class?

  1. Sum the number of pupils from the table.

    Total number of pupils=11+10+1+4+8\text{Total number of pupils} = 11 + 10 + 1 + 4 + 8 Total number of pupils=34\text{Total number of pupils} = 34

    The total number of people in the class is 34\boxed{\text{34}}.

Part b

517\frac{5}{17}

What is the probability of a pupil who scored 10 marks?

  1. Identify the number of pupils who scored 10 marks.

    From the table, the number of pupils who scored 10 marks is 10.

  2. Calculate the probability.

    P(scored 10 marks)=Number of pupils who scored 10 marksTotal number of pupilsP(\text{scored 10 marks}) = \frac{\text{Number of pupils who scored 10 marks}}{\text{Total number of pupils}} P(scored 10 marks)=1034P(\text{scored 10 marks}) = \frac{10}{34}

  3. Simplify the fraction.

    P(scored 10 marks)=517P(\text{scored 10 marks}) = \frac{5}{17}

    The probability of a pupil scoring 10 marks is 517\boxed{\frac{5}{17}}.

Part c(i)

534\frac{5}{34}

less than 8 marks

What is the probability that a pupil chosen at random from the class scored...

  1. Identify the marks less than 8 and their corresponding number of pupils.

    Marks less than 8 are 1 and 4.
    Number of pupils for 1 mark = 1.
    Number of pupils for 4 marks = 4.

  2. Calculate the total number of pupils who scored less than 8 marks.

    Number of pupils (less than 8 marks)=1+4=5\text{Number of pupils (less than 8 marks)} = 1 + 4 = 5

  3. Calculate the probability.

    P(scored less than 8 marks)=534P(\text{scored less than 8 marks}) = \frac{5}{34}

    The probability that a pupil scored less than 8 marks is 534\boxed{\frac{5}{34}}.

Part c(ii)

1134\frac{11}{34}

more than 10 marks

  1. Identify the marks more than 10 and their corresponding number of pupils.

    The only mark more than 10 is 11.
    Number of pupils for 11 marks = 11.

  2. Calculate the probability.

    P(scored more than 10 marks)=1134P(\text{scored more than 10 marks}) = \frac{11}{34}

    The probability that a pupil scored more than 10 marks is 1134\boxed{\frac{11}{34}}.

Part c(iii)

2134\frac{21}{34}

at least 10 marks

  1. Identify the marks at least 10 and their corresponding number of pupils.

    Marks at least 10 are 10 and 11.
    Number of pupils for 10 marks = 10.
    Number of pupils for 11 marks = 11.

  2. Calculate the total number of pupils who scored at least 10 marks.

    Number of pupils (at least 10 marks)=10+11=21\text{Number of pupils (at least 10 marks)} = 10 + 11 = 21

  3. Calculate the probability.

    P(scored at least 10 marks)=2134P(\text{scored at least 10 marks}) = \frac{21}{34}

    The probability that a pupil scored at least 10 marks is 2134\boxed{\frac{21}{34}}.

Part c(iv)

534\frac{5}{34}

at most 4 marks

  1. Identify the marks at most 4 and their corresponding number of pupils.

    Marks at most 4 are 1 and 4.
    Number of pupils for 1 mark = 1.
    Number of pupils for 4 marks = 4.

  2. Calculate the total number of pupils who scored at most 4 marks.

    Number of pupils (at most 4 marks)=1+4=5\text{Number of pupils (at most 4 marks)} = 1 + 4 = 5

  3. Calculate the probability.

    P(scored at most 4 marks)=534P(\text{scored at most 4 marks}) = \frac{5}{34}

    The probability that a pupil scored at most 4 marks is 534\boxed{\frac{5}{34}}.

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