09:35 7 101 4G 2 of 3 ematics . 1 of 3 05/1 1/20 @ MEI ..da@12100000838740661 from Courmaligraineauand3 04-2022 03:35:26 GMT -06:00 Innovation https://www.coursehero.com/file/83825998/probability-integralpdf/ MEI AS Maths Probability Assessment 4. The Venn diagram shows two events, A and B, and their associated probabilities. B 0.6 0.2 Given that events A and B are independent, find the values of p and q. [3] 5. The students in a school sixth form were asked for their most common mode of transport to school. The replies are summarised in the table below. Mode of transport Walk/Cycle Public Private car Total transport 44 72 Year Group Year 12 16 132 Year 13 40 63 17 120 Total 84 135 33 252 (a) Two students are randomly selected. What is the probability that they are in different year groups? [2] (b) Two students are randomly selected. What is the probability that they are in different year groups but are in the same "mode of transport' category? [3] (c) Based on the data given in the table, are the events 'in Year 12' and 'walk/cycle to school' independent? Clearly explain your reasoning. [3] 6. A practical music examination can be taken once or twice. Those candidates who fail it on the first occasion take it a second time. For those having their first attempt, 25% pass with distinction and 45% gain an ordinary pass. For those taking the examination for a second time, the corresponding figures are 5% and 70% respectively. The tree diagram below illustrates the situation. 2 of 3 05/1 1/20 @ MEI This study source was downloaded by 100000838740661 from Courallgrajmeanandly 04-2022 03:35:26 GMT -06:00 https:/www.coursehero.com/file/83825998/probability-integralpdf/ MEI AS Maths Probability Assessment First Second attempt attempt Pass with Distinction Ordinary Pass with Pass Distinction coursehero.com09:35 4 1 4G off the first occasion take it a second time. For those having their first attempt, 25% pass with distinction and 45% gain an ordinary those taking the examination for a second time, the corresponding figures are 3 of 3 70% respectively. The tree diagram below illustrates the situation. 2 of 3 05/1 1/20 @ MEI This study source was downloaded by 100000838740661 from Courallgrainsaundra 04-2022 03:35:26 GMT -06:00 https://www.coursehero.com/file/83825998/probability-integralpdf/ MEI AS Maths Probability Assessment First Second attempt attempt Pass with Distinction Ordinary Pass with Pass Distinction Ordinary Fail Pass Fail (a) Find the probability that, following a second attempt if needed, a randomly chosen candidate: (i) fails the examination (ii) passes the examination (with or without distinction) [4] Jill and Jo are two randomly chosen entrants for the examination. Find the probabilities that (i) both pass (with or without distinction), but just one of them needs a second attempt, (ii) Jill gets a better result than Jo. [8] Total 40 marks 3 of 3 05/1 1/20 @ MEI This study source was downloaded by 100000838740661 from Courmigrainepu only 04-2022 03:35:26 GMT -06:00 coursehero.com C m09:35 4 101 4G 1 of 3 MEI AS Mathematics Probability "integral' Topic assessment 1. In this question you must show detailed reasoning. Which is more likely, never getting a 6 when rolling a fair die six times, or never getting a double 6 when rolling a pair of fair dice 36 times? [4] 2. In the sixth form at Eastport School, there are 45 students studying at least one of the three sciences, Biology, Chemistry and Physics. The diagram below shows the number of students studying each science. Biology Chemistry 12 15 Physics (a) Find the probability that one of these students, selected at random, is studying (i) Physics (ii) Chemistry (iii) both Physics and Chemistry. [3] (b) Two students are selected at random. Find the probability that both are studying just one science and that they are not both studying the same science. [4] 3. The probability distribution of a discrete random variable X is given by: P(X = r) = k(62 -73) for r = 1, 2, 3, 4, 5 P(X = r) =0 otherwise (a) Show that k = = [3] 105 Two values of X are chosen at random. (b) Find the probability that the product of the two values is even. [3] M Mathematics . Education100000838740661 from Courallgrainsamendly 04-2022 03:35:26 GMT -06:00 1 of 3 05/1 1/20 @ MEI Innovation https://www.coursehero.com/file/83825998/probability-integralpdf? MEI AS Maths Probability Assessment 4. The Venn diagram shows two events, A and B, and their associated probabilities. coursehero.com C