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Name Date Unit Test: Unit 11 Probability 1. A jar is filled with 48 yellow jelly beans, 43 red jelly beans, 52 orange jelly beans, and 57 green jelly beans. One jelly bean is picked at random. a) What are the possible outcomes? b) What is the probability of picking each colour of jelly bean? 2. A regular tetrahedron is labelled 1 to 4. A number cube is labelled 1 to 6. The tetrahedron and cube are rolled. a) Record the numbers on the faces that do not show. Are you more likely to get the answer 8 if you add these numbers or multiply them? Explain your answer. _________________________________________________________ _________________________________________________________ _________________________________________________________ b) Make up your own problem about the tetrahedron and cube. Solve the problem. Show your work. 40 3. Each of two spinners has congruent sectors. Spinner A has 4 sectors coloured red, green, yellow, and black. Spinner B has 3 sectors coloured red, green, and purple. a) The pointer on each spinner is spun. Use a tree diagram to list the possible outcomes. b) What is the probability that the colours are different? Explain. c) What is the probability that only one colour is red? Explain. d) What is the probability that no colour is red? Explain. e) What is the probability that no colour is orange? Explain. 47 4. a) In her 85 times at bat, Jillian got 55 hits. What is her batting average? b) A home cleaning service solicits new business by telephone. On one day, 500 telephone calls were made. They produced 111 new customers. What is the relative frequency of getting a customer over the phone? Explain. c) A quality controller at a battery manufacturing company tested 360 batteries from the production line. She found that 19 were defective. A box contains 5000 batteries. How many might you expect not to be defective? Show two different ways to solve this problem. 47 Name Master 11.12 Date Sample Answers Unit Test – Master 11.11 1. a) b) 2. a) b) 3. a) Yellow, red, orange, green The total number of jelly beans is 200: 48 + 43 + 52 + 57 = 200. The probability of picking a: 48 6 yellow jelly bean is = or 0.24 200 25 43 red jelly bean is or about 0.22 200 52 13 orange jelly bean is = or 0.26 200 50 57 green jelly bean is or 0.28 200 Students can draw addition and multiplication tables. There are 2 ways to get 8 if you multiply: 2 4 and 4 2. There are 3 ways to get 8 if you add: 6 + 2, 5 + 3, 4 + 4. So, you are more likely to get 8 if you add the numbers that show. Sample problem: You can divide the number on the cube by the number on the tetrahedron, or you can subtract the number on the tetrahedron from the number on the cube. With which operation are you more likely to get the answer 2? Solution: There are 3 ways to get the answer 2 if you divide: 2 1, 4 2, 6 3. There are 4 ways to get the answer 2 if you subtract: 3 – 1, 4 – 2, 5 – 3, 6 – 4. So, you are more likely to get 2 if you subtract. b) c) d) e) 4. a) b) c) 10 5 = ; 10 out of 12 outcomes have 12 6 2 different colours. 5 ; 5 out of 12 outcomes have only 1 red sector. 12 6 1 = ; 6 out of 12 outcomes have no red sectors. 12 2 1; there are no orange sectors, so all outcomes never have orange. 55 =˙ 0.647, or approximately 65% 85 111 =˙ 0.222, or approximately 22% 500 Solution Method 1: 19 are defective, so 360 – 19 = 341 are not defective. So, the probability of not being defective is 341 =˙ 0.947. 360 Multiply the probability by the number of 341 batteries. 5000 =˙ 4736 360 So, approximately 4736 batteries should not be defective. Solution Method 2: The probability of being 19 defective is =˙ 0.053. 360 Find out how many batteries will be defective. Multiply the probability of being defective by 5000. 19 5000 =˙ 263.9 or approximately 360 264 batteries will be defective. The number of non-defective batteries will be 5000 – 264 = 4736. So, approximately 4736 batteries should not be defective. 48