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Year 9 SAT Revision Probability Questions Levels 6, 7 & 8 1. Level 6 Probability (a) A bag has 20 cubes in it. 6 of the cubes are green. You take one cube out of the bag at random. Which values below show the probability that you take out a cube that is green? Circle the correct four values. 6 30% 0.6 3/10 14 6% 3/5 6/20 0.03 0.3 6/10 60% 6 26 2 marks (b) A box has 20 counters in it. 11 of the counters are red. You take one counter out of the box at random. What is the probability that the counter you take out is not red? Write your answer as a fraction. 1 mark Now write your answer as a percentage. 1 mark Total 4 marks Fallibroome High School 1 2. Level 6 Doubles I have two fair dice. Each of the dice is numbered 1 to 6. (a) The probability that I will throw double 6 (both dice showing number 6) is 1 36 What is the probability that I will not throw double 6? 1 mark (b) I throw both dice and get double 6. Then I throw the dice again. Tick the box that describes the probability that I will throw double 6 this time. less than 1 36 1 36 more than 1 36 Explain your answer. 1 mark I start again and throw both dice. (c) What is the probability that I will throw double 3 (both dice showing 3)? 1 mark (d) What is the probability that I will throw a double? (It could be double 1 or double 2 or any other double.) 1 mark Fallibroome High School 2 3. Level 7 Throw Some pupils threw 3 fair dice. They recorded how many times the numbers on the dice were the same. Number Results Name of throws all different 2 the same all the same Morgan 40 26 12 2 Sue 140 81 56 3 Zenta 20 10 10 0 Ali 100 54 42 4 (a) Write the name of the pupil whose data are most likely to give the best estimate of the probability of getting each result. ………………… Explain your answer. 1 mark (b) This table shows the pupils’ results collected together: Number Results of throws all different 2 the same all the same 300 171 120 9 Use these data to estimate the probability of throwing numbers that are all different. 2 marks Fallibroome High School 3 (c) The theoretical probability of each result is shown below: all different 2 the same all the same Probability 5 5 1 9 12 36 Use these probabilities to calculate, for 300 throws, how many times you would theoretically expect to get each result. Number Theoretical results of throws all different 2 the same all the same 300 ............... ............... ............... 1 mark (d) Explain why the pupils’ results are not the same as the theoretical results. 1 mark 4. Level 7 Experiment Barry is doing an experiment. He drops 20 matchsticks at random onto a grid of parallel lines. Barry does the experiment 10 times and records his results. He wants to work out an estimate of probability. Number of the 20 matchsticks that have fallen across a line 5 7 6 4 6 8 5 3 5 7 (a) Use Barry’s data to work out the probability that a single matchstick when dropped will fall across one of the lines. Show your working. .............................. 2 marks Fallibroome High School 4 (b) Barry continues the experiment until he has dropped the 20 matchsticks 60 times. About how many matchsticks in total would you expect to fall across one of the lines? Show your working. ............................... matchsticks 2 marks 5. Level 7 A headteacher wants to choose a pupil from year 7, 8 or 9 to appear on television. The headteacher gives each pupil one ticket. Then she will select the winning ticket at random. The table shows information about the ticket used. Colour of Numbers the ticket used Year 7 red 1 to 80 Year 8 blue 1 to 75 Year 9 yellow 1 to 90 (a) What is the probability that the winning ticket will be blue? 1 mark (b) What is the probability that the winning ticket will show number 39? 1 mark (c) The headteacher selects the winning ticket at random. She says: ‘The winning ticket number is 39’. What is the probability that this winning ticket is blue? 1 mark Fallibroome High School 5 6. Level 7 Questions A box contains cards with one question on each card. There are 4 categories of questions. Each category has some easy and some difficult questions. The table shows the probability of selecting a card at random from the box. Category Easy Difficult Music 0.2 0.15 Sport 0.2 0.1 History 0.1 0.05 Nature 0.15 0.05 (a) I am going to take one card at random from the box. What is the probability that it will be a history question? ..................... 1 mark an easy question? ..................... 1 mark (b) There are 40 cards in the box. How many of these are music questions? ..................... 1 mark Fallibroome High School 6 7. Level 8 Brightlite company makes light bulbs. The state of the company’s machines can be: available for use and being used or available for use but not needed or broken down. (a) The table shows the probabilities of the state of the machines in July 1994. Write in the missing probability. State of machines: July 1994 Probability Available for use, being used Available for use, not needed 0.09 Broken down 0.03 1 mark (b) During another month the probability of a machine being available for use was 0.92. What was the probability of a machine being broken down? .............................. 1 mark (c) Brightlite calculated the probabilities of a bulb failing within 1000 hours and within 2000 hours. Complete the table below to show the probabilities of a bulb still working at 1000 hours and at 2000 hours. Time Failed Still working At 1000 hours 0.07 At 2000 hours 0.57 1 mark (d) Calculate the probability of two bulbs both failing within 1000 hours. .............................. 1 mark (e) Calculate the probability of two bulbs both still working at 2000 hours. .............................. Fallibroome High School 7 1 mark 8. Level 8 What number? I have a bag that contains blue, red, green and yellow counters. I am going to take out one counter at random. The table shows the probability of each colour being taken out. Blue Red Green Yellow Probability 0.05 0.3 0.45 0.2 (a) Explain why the number of yellow counters in the bag cannot be 10 1 mark (b) What is the smallest possible number of each colour of counter in the bag? Blue Red Green Yellow 2 marks 9. Level 8 Disks A company makes computer disks. It tested a random sample of disks from a large batch. The company calculated the probability of any disk being defective as 0.025. Glenda buys two disks. (a) Calculate the probability that both disks are defective. ............................... 1 mark (b) Calculate the probability that only one of the disks is defective. ............................... cm 2 marks Fallibroome High School 8 (c) The company found 3 defective disks in the sample they tested. How many disks were likely to have been tested? About .............................. disks. 1 mark 10. Level 8 Languages 100 students were asked whether they studied French or German. French German 39 27 30 4 27 students studied both French and German. (a) What is the probability that a student chosen at random will study only one of the languages? 1 mark (b) What is the probability that a student who is studying German is also studying French? 1 mark (c) Two of the 100 students are chosen at random. Circle the calculation which shows the probability that both the students study French and German? 27 26 27 26 27 27 100 100 100 99 100 100 27 26 27 27 100 100 100 100 1 mark Fallibroome High School 9