This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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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: |c|c| MARKS IN & Number of pupils \\ 11 & 11 \\ 10 & 10 \\ 1 & 1 \\ 4 & 4 \\ 8 & 8 \\ a) How many people are in the class? Step 1: Sum the number of pupils from the table. Total number of pupils = 11 + 10 + 1 + 4 + 8 Total number of pupils = 34 The total number of people in the class is 34. b) What is the probability of a pupil who scored 10 marks? Step 1: Identify the number of pupils who scored 10 marks. From the table, the number of pupils who scored 10 marks is 10. Step 2: Calculate the probability. P(scored 10 marks) = Number of pupils who scored 10 marksTotal number of pupils P(scored 10 marks) = (10)/(34) Step 3: Simplify the fraction. P(scored 10 marks) = (5)/(17) The probability of a pupil scoring 10 marks is (5)/(17). c) What is the probability that a pupil chosen at random from the class scored... i) less than 8 marks Step 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. Step 2: Calculate the total number of pupils who scored less than 8 marks. Number of pupils (less than 8 marks) = 1 + 4 = 5 Step 3: Calculate the probability. P(scored less than 8 marks) = (5)/(34) The probability that a pupil scored less than 8 marks is (5)/(34). ii) more than 10 marks Step 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. Step 2: Calculate the probability. P(scored more than 10 marks) = (11)/(34) The probability that a pupil scored more than 10 marks is (11)/(34). iii) at least 10 marks Step 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. Step 2: Calculate the total number of pupils who scored at least 10 marks. Number of pupils (at least 10 marks) = 10 + 11 = 21 Step 3: Calculate the probability. P(scored at least 10 marks) = (21)/(34) The probability that a pupil scored at least 10 marks is (21)/(34). iv) at most 4 marks Step 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. Step 2: Calculate the total number of pupils who scored at most 4 marks. Number of pupils (at most 4 marks) = 1 + 4 = 5 Step 3: Calculate the probability. P(scored at most 4 marks) = (5)/(34) The probability that a pupil scored at most 4 marks is (5)/(34).