7 A bag contains coloured counters. A counter is taken from the bag at random. The table shows the probabilities of taking a counter of each colour. Colour Red Green Blue Yellow Probability 0.15 0.3 0.42 Complete the table. [2]

7 0.13 2 M1 for 1 – (0.15 + 0.3 + 0.42) or B1 for 0.87 seen To earn full marks, you must correctly calculate the probability as 0.13. You can earn one mark by showing the calculation 1 minus the sum of the given probabilities (0.15 + 0.3 + 0.42), or by correctly calculating the sum of the given probabilities as 0.87.

11 (a) In a survey, 3 out of every 100 women were taller than 1.9 m. One of these 100 women is picked at random. Calculate the probability that she is not taller than 1.9 m. … [1] (b) A new housing estate is being planned. There are three possible plans: A, B and C. A survey was carried out to see which plan people preferred. The relative frequency table shows the results. Plan A B C Relative frequency 0.3 0.5 0.2 52 people preferred plan C. (i) Find how many people preferred plan A. … [2] (ii) Calculate the total number of people surveyed. … [1]

11(a) 0.97 or 97 100 1 11(b)(i) 78 2 M1 for 52 ÷ [0.]2 oe or 52 × 1.5 oe 11(b)(ii) 260 1 For part (a), you must state the probability as 0.97 or 97/100. For part (b)(i), you must correctly find the number of people who preferred plan A; one mark is awarded for correctly dividing 52 by 0.2 or multiplying 52 by 1.5. For part (b)(ii), you must correctly state the total number of people surveyed.

19 (a)  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} X = {2, 3, 5, 7, 11} Y = {1, 2, 3, 4, 5, 6} (i) Find X Y + . { … } [1] (ii) A number, k, is chosen at random from . Find the probability that ( ) k X Y , g . … [1] (b) On the Venn diagram, shade the set ( ) A B C + , l . A B C [1]

19(a)(i) 2, 3, 5 1 19(a)(ii) 4 12 oe 1 19(b) 1 (a)(i) To earn marks, you must list the elements common to both sets X and Y. (a)(ii) To earn marks, you must state the probability as the number of elements in the intersection of X and Y divided by the total number of elements in the universal set. (b) To earn marks, you must shade the region representing the complement of the union of sets A and B, intersected with C.

2 A survey recorded the number of people living in each of 50 houses. The bar chart shows the results. 0 1 2 3 4 Number of people Frequency 5 6 2 4 6 8 10 12 14 (a) Find the mode. … [1] (b) Find the median. … [1] (c) Calculate the mean. … [3] (d) One of these houses is chosen at random. Find the probability that exactly 3 people live there. … [1] (e) Two houses are chosen at random from these 50 houses. Find the probability that only one of the two houses has exactly 5 people living there. … [3]

2(a) 4 1 2(b) 3 1 2(c) 3.22 or 3 11 50 3 B1 for 7, 11, 10, 12, 6, and 4 soi M1 for 7 1 11 2 10 3 12 4 6 5 4 6 50 × + × + × + × + × + × 2(d) 10 50 oe 1 2(e) 264 1225 oe 3 M2 for [ ] 6 44 2 50 49 × × or M1 for [ ] 50 2 50 49 − × × a a where 0 < a < 50 After 0 scored, SC1 for answer 528 2500 oe (a) To earn marks, you must identify the number of people with the highest frequency from the bar chart. (b) To earn marks, you must find the middle value of the number of people when the data is ordered. (c) To earn marks, you must correctly calculate the sum of (frequency × number of people) for all categories and divide by the total number of houses. (d) To earn marks, you must state the probability as the number of houses with 3 people divided by the total number of houses, in its simplest form. (e) To earn marks, you must calculate the probability of choosing one house with 5 people and one house without 5 people, considering both possible orders, and simplify the fraction.

4 100 adults in a town were surveyed about the number of emails they each received one day. The table shows the results. Number of emails 1 2 3 4 5 6 7 8 Number of adults 8 10 22 28 15 9 5 3 (a) Find the mode. … [1] (b) Calculate the mean. … [2] (c) One of these adults is chosen at random. Find the probability that they received fewer than 4 emails that day. Give your answer as a fraction in its simplest form. … [2] (d) The town has 18 000 adults. Use the survey results to estimate the number of adults in the town who received exactly 5 emails that day. … [2]

4(a) 4 1 4(b) 3.94 or 3 94 100 or 3 47 50 2 M1 for 1 8 2 10 3 22 4 28 5 15 6 9 7 5 8 3 100 × + × + × + × + × + × + × + × 4(c) 2 5 cao 2 B1 for 8 10 22 100 + + oe After 0 scored, SC1 for answer 17 25 4(d) 2700 2 M1 for 15 100 [× 18 000] oe (a) To earn marks, you must identify the number of emails that has the highest frequency. (b) To earn marks, you must show the sum of (number of emails × number of adults) for all categories, divided by the total number of adults (100). (c) To earn marks, you must sum the number of adults who received 1, 2, or 3 emails, place this sum over the total number of adults (100), and then simplify the resulting fraction. (d) To earn marks, you must calculate the proportion of adults who received exactly 5 emails from the survey and multiply this proportion by the total number of adults in the town.

Cambridge O Level Mathematics (Syllabus D) · 4024

O-Level Mathematics (Syllabus D) (4024) Probability past paper questions

Revise O-Level Mathematics (Syllabus D) (4024) — Probability with real Cambridge past-paper questions grouped by topic, each shown with its marking scheme. Working one topic at a time targets exactly the skill each question tests.

45 free questions from 2016–2021, each with its marking scheme. Open the full topical bank to filter by subtopic, paper, and year.