Can you please answer those math questions and show your work? Put and show the steps and how you got the answer. If you need you can do it on a piece of paper and attach it. But it is so important to show your work and the steps of how you got the answers to the questions and make it clear.

The questions:

2. Jim drives to work each day through two sets of traffic lights. The probability of the first set of traffic lights being red is 0.65. If the first set is red then the probability that the next set of traffic lights is red is 0.46. If the first set is not red, the probability that the next set is red is 0.72. red red 0.65 not red red not red not red (a) Complete the tree diagram above. (b) Calculate the probability that the second set of traffic lights is red. (Total 8 marks) Working: Answers: (a) (b) IB Questionbank Mathematical Studies 3rd edition 23. Sharon and Lisa share a at. Sharon cooks dinner three nights out often. If Sharon does not cook dinner. then Lisa does If Sharon cooks dinner the probability that they have pasta is 0.15. If Lisa cooks dinner the probability that they have pasta is 0.12. (a) Copy and complete the tree diagram to represent this information. Pasta 0.75 Not Pasta Pasta Not Pasta (3) (b) Find the probability that Lisa cooks dinner and they do not have pasta. (2) (c) Find the probability that they do not have pasta. (3) {d} Given that they do not have pasta. nd the probability that Lisa cooked dinner. (3) t6 Questionoank Mathematical Studies 3rd edition 3 4. Amos travels to school either by car or by bicycle. The probability of being late for school is - if he 10 travels by car and > if he travels by bicycle. On any particular day he is equally likely to travel by car or by bicycle. (a) Draw a probability tree diagram to illustrate this information. (4) (b) Find the probability that (i) Amos will travel by car and be late. (2) (ii) Amos will be late for school. (3) (c) Given that Amos is late for school, find the probability that he travelled by bicycle. (3) Total 12 marks) Working: Answers: (b) (i) ..... (11) ..... (c IB Questionbank Mathematical Studies 3rd edition5. A bag contains two red sweets and three green sweets. Jacques takes one sweet from the bag, notes its colour. then eats it. He then takes another sweet from the bag. Complete the tree diagram below to Show all probabilities. Red 2 Red 5 Green Red A 4 Green Green (Total 4 marks) J'B Questionbc'mk Mathema'kzl Studies 3rd edition 5 6. When Andy plays tennis, 65% of his first serves go into the correct area of the court. If the first serve goes into the correct area, his chance of winning the point is 90%. If his first serve does not go into the correct area, Andy is allowed a second serve and, of these, 80% go into the correct area. If the second serve goes into the correct area, his chance of winning the point is 60%. If neither serve goes into the correct area, Andy loses the point. (a) Complete the tree diagram below. . Win First serve in 0.65 0.1 Lose 0.6 Win Second 0.35 serve First 0.8 in 0.4 serve - Lose out 0.2 Second serve out - Lose (2) (b) Find the probability that Andy loses the point. (4) (Total 6 marks) Working: Answers: (b IB Questionbank Mathematical Studies 3rd edition 67. Claire and Kate both Wish to go to the cinema but one of them has to stay at home to baby-sit. The probability that Kate goes to the cinema is 0.2. If Kate does not go Claire goes. If Kale goes to the cinema the probability that she is late home is 0.3' IfClaire goes to the cinema the probability that she is late home is 0.6. (a) Copy and complete the probability tree diagram below. Late Kate Not Late Late Claire Not Late (3) (b) Calculate the probability that (i) Kate goes to the cinema and is not late; (7) (ii) the person who goes to the cinema arrives heme later Armrers: (b)(i] ............................................................................... t8 Ouestionbank Mathematical Studies 3rd edition 7 8. Neil has three dogs. Two are brown and one is grey. When he feeds the dogs, Neil uses three bowls and gives them out randomly. There are two red bowls and one yellow bowl. This information is shown on the tree diagram below. E Red 3 E Brown I 3 3 Yellow 1 E Red 5 are 3 1 A _ 3 hello\" (a) One of the dogs is chosen at random. (i) Find P (the dog is grey and has the yellow bowl). (ii) Find P (the dog does not get the yellow bowl}. (3) (b) Neil often takes the dogs to the pad: after they have eaten. He has noticed that the grey dog plays with a stick for a quarter of the time and both brown dogs play with slicks for half of the time. This information is shown on the tree diagram below. 3m 2 3 Brown No stick 1 Stick 3 Gm No stiti (i) Copy the tree diagram and add the four missing probability values on the branches that refer to playing with a stick. During a trip to the park, one ofthe dogs is chosen at random. (ii) Find P (the dog is grey or is playing with a stick, but not both). (iii) Find P (the dog is grey given that the dog is playing with a stick}. (iv) Find P (the dog is grey and was fed from the yellow bowl and is not playing with a stick). (9) (Total 12 marks) i'B Otiest'ionbak Whematkai Studies 3N edition 8 9. When Geraldine travels to work she can travel either by car (C), bus (B) or train (7). She travels by car on one day in five. She uses the bus 50% of the time. The probabilities of her being late (Z) when travelling by car, bus or train are 0.05, 0.12 and 0.08 respectively. (a) Copy the tree diagram below and fill in all the probabilities, where ML represents not late, to represent this information. (5) 0.2 NL L B NL L NL (b) Find the probability that Geraldine travels by bus and is late. (1) (c) Find the probability that Geraldine is late. (3) (d) Find the probability that Geraldine travelled by train, given that she is late. (3) (Total 12 marks) IB Questionbank Mathematical Studies 3rd edition 9Practice: Tree diagrams Name: l. The probability that it rains today is 0.4. If it rains today. the probability that it will rain tomorrow is 0.8. If it does not rain today. the probability that it will rain tomorrow is 0.7. (a) Complete the tree diagram below. Today Tomorrow .8 Rain Rain L _ Nu Rain Rain _ Nu Rain _ No Rain (3) [b] Calculate the probability of rain tomorrow. (3) Working: Answers: (a) .'B Ousstt'onbank Mathematics! Studies 3rd edition 1