2016 2014 CAPS Probability WC

Western Cape Education Department Examination Preparation Learning Resource 2016 Probability MATHEMATICS Grade 12 Razzia Ebrahim Senior Curriculum Planner for Mathematics E-mail: Razzia.Ebrahim@wced.info/ Razzia.Ebrahim@westerncape.gov.za Website: http://www.wcedcurriculum.westerncape.gov.za/index.php/component/jdownloads/category/1835- grade-12?Itemid=-1 Website: http://wcedeportal.co.za Tel: 021 467 2617 Cell: 083 708 0448

Index Page 1. 2016 June Paper 1 3 2. 2016 Feb-March Paper 1 4 3. 2015 November Paper 1 5 4. 2015 June Paper 1 6 5. 2015 Feb-March Paper 1 7–8 6. 2014 November Paper 1 9 7. 2014 Exemplar Paper 1 10 2

DBE/2016 10.2 The probability of events A and B occurring are denoted by P(A) and P(B) respectively. For any two events A and B it is given that:  P( B ) = 0,28  P(B) = 3P(A)  P(A or B) = 0,96 Are events A and B mutually exclusive? Justify your answer. (4) [10] QUESTION 11 Five boys and four girls go to the movies. They are all seated next to each other in the same row. 11.1 One boy and girl are a couple and want to sit next to each other at any end of the row of friends. In how many different ways can the entire group be seated? (3) 11.2 If all the friends are seated randomly, calculate the probability that all the girls are seated next to each other. (3) [6] Copyright reserved 3

QUESTION 10 DBE/Feb.—Mar. 2016 10.1 Each passenger on a certain Banana Airways flight chose exactly one beverage from tea, coffee or fruit juice. The results are shown in the table below. MALE FEMALE TOTAL Tea 20 40 60 Coffee b c 80 Fruit juice d e 20 TOTAL 60 100 a 10.1.1 Write down the value of a. 10:12 What is the probability that a randomly selected passenger is male? 10.1.3 Given that the event of a passenger choosing coffee is independent of being a male, calculate the value of 5. 10.2 A Banana Airways aeroplane has 6 seats in each row. 10.2.1 How many possible arrangements are there for 6 people to sit in a row of 6 seats? 10.2.2 Xoliswa, Anees and 4 other passengers sit in a certain row on a Banana Airways flight. In how many different ways can these 6 passengers be seated if Xoliswa and Anees must sit next to each other? 10.2.3 Mary and 5 other passengers are to be seated in a certain row. If seats are Copyright reserved allocated at random, what is the probability that Mary will sit at the end of the row? (1) (2) (4) 2) (2) (4) [15]

DBE/November 2015 QUESTION 11 11.1 For two events, A and B, it is given that: P(A) = 0,2 P(B) = 0,63 P(A and B) = 0,126 Are the events, A and B, independent? Justify your answer with appropriate calculations. (3) 11.2 The letters of the word DECIMAL are randomly arranged into a new ‘word', also consisting of seven letters. How many different arrangements are possible if: 11.2.1 Letters may be repeated (2) 11.2.2 Letters may not be repeated (2) TL.2:3 The arrangements must start with a vowel and end in a consonant and no repetition of letters is allowed (4) 11.3 There are ¢ orange balls and 2 yellow balls in a bag. Craig randomly selects one ball from the bag, records his choice and returns the ball to the bag. He then randomly selects a second ball from the bag, records his choice and returns it to bag. It is known that the probability that Craig will select two balls of the same colour from the bag is 52%, Calculate how many orange balls are in the bag. (6) (17] Copyright reserved

DBE/2015 QUESTION 11 11.1 Zebra High School offers only two sporting activities, namely rugby and hockey. The following information is given: There are 600 learners in the school. 372 learners play hockey. 288 learners play rugby. 56 of the learners play NO sport. The number of learners that play both hockey and rugby is x. 11.1.1 Represent the given information in a Venn diagram, in terms of x. 11.1.2 Calculate the value of x. 11.1.3 Are the events playing rugby and playing hockey mutually exclusive? Justify your answer. 11.2 Another school, Tulani High, has a sports awards ceremony. Tulani High has a basketball team consisting of 5 players and a volleyball team consisting of 6 players. 11.2.1 All the basketball players sit in a single row at the ceremony. There are no restrictions on who sits in which position. In how many different ways can they be seated? 11.2.2 The decision is taken that the captain must sit in the first seat of the row. The two vice-captains have to be seated next to each other in any of the remaining seats. In how many different ways can the basketball players be seated now? 11.2.3 After the interval, the basketball team and the volleyball team sit in the same row at the ceremony. Calculate the probability that the basketball players will sit together and the volleyball players will sit together. Assume that seating positions are allocated randomly. Give your answer as a simplified fraction. Copyright reserved (3) (2) (2) Q) (3) (3) [14]

DBE/Feb.—Mar. 2015 QUESTION 10 10.1 Research was conducted about driving under the influence of alcohol. Information obtained from traffic authorities in 54 countries on the methods that are used to measure alcohol levels in a person, are summarised below: e 4 countries use all three methods (A, B and C). © 12 countries use the alcohol content of breath (A) and blood-alcohol concentration (B). e 9 countries use blood-alcohol concentration (B) and certificates issued by doctors (C). e 8 countries use the alcohol content of breath (A) and certificates issued by doctors (C). 21 countries use the alcohol content of breath (A). 32 countries use blood-alcohol concentration (B). 20 countries use certificates issued by doctors (C). 6 countries use none of these methods. Below is a partially completed Venn diagram representing the above information. S c B (xX 6 A 10.1.1 Use the given information and the Venn diagram to determine the values of d, e, f and g. (4) 10.1.2 For a randomly selected country, calculate: (a) P(A and Band C) (1) (b) P(A or B or C) Q) (c) P(only C) dd) (d) P(that a country uses exactly two methods) (1) Copyright reserved Please turn over

10.2 DBE/Feb.—Mar. 2015 Nametso may choose DVDs from three categories as listed in the table below: Drama Romance Comedy © Last Hero One Heart e Laughing Dragon e Midnight You and Me e Falling Down e Stranger Calls Love Song e Sitting on the Stairs e Missing in Action Bird's First Nest e Only 40 Seconds Left 10.2.1 Nametso must choose ONE DVD from the Drama category. What is the probability that she will choose Midnight? (2) 10.2.2 How many different selections are possible if her selection must include ONE drama, ONE romance and ONE comedy? (2) 10.2.3 Calculate the probability that she will have Last Hero and Laughing Dragon as part of her selection in QUESTION 10.2.2. (2) (14) Copyright reserved

Mathematics/P1 DBE/November 2014 NSC QUESTION 11 A survey concerning their holiday preferences was done with 180 staff members. The options they could choose from were to:  Go to the coast  Visit a game park  Stay at home The results were recorded in the table below: Coast Game Park Home Total Male 46 24 13 83 Female 52 38 7 97 Total 98 62 20 180 11.1 Determine the probability that a randomly selected staff member: 11.1.1 Is male (1) 11.1.2 Does not prefer visiting a game park (2) 11.2 Are the events 'being a male' and 'staying at home' independent events. Motivate your answer with relevant calculations. (4) [7] QUESTION 12 12.1 A password consists of five different letters of the English alphabet. Each letter may be used only once. How many passwords can be formed if: 12.1.1 All the letters of the alphabet can be used (2) 12.1.2 The password must start with a 'D' and end with an 'L' (2) 12.2 Seven cars of different manufacturers, of which 3 are silver, are to be parked in a straight line. 12.2.1 In how many different ways can ALL the cars be parked? (2) 12.2.2 If the three silver cars must be parked next to each other, determine in how many different ways the cars can be parked. (3) [9] Copyright reserved 9

Mathematics/P1 DBE/2014 NSC – Grade 12 Exemplar QUESTION 11 11.1 Events A and B are mutually exclusive. It is given that: • P(B) = 2P(A) • P(A or B) = 0,57 Calculate P(B). (3) 11.2 Two identical bags are filled with balls. Bag A contains 3 pink and 2 yellow balls. Bag B contains 5 pink and 4 yellow balls. It is equally likely that Bag A or Bag B is chosen. Each ball has an equal chance of being chosen from the bag. A bag is chosen at random and a ball is then chosen at random from the bag. 11.2.1 Represent the information by means of a tree diagram. Clearly indicate the probability associated with each branch of the tree diagram and write down all the outcomes. (4) 11.2.2 What is the probability that a yellow ball will be chosen from Bag A? (1) 11.2.3 What is the probability that a pink ball will be chosen? (3) [11] QUESTION 12 Consider the word M A T H S. 12.1 How many different 5-letter arrangements can be made using all the above letters? (2) 12.2 Determine the probability that the letters S and T will always be the first two letters of the arrangements in QUESTION 12.1. (3) [5] Copyright reserved 10