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1 a Explain how fractions can be added and subtracted. Give some examples. b A spinner has sections labelled A, B, C and D. The probability of getting A is getting B is 2 1 5 1 4 , and the probability of . What is the total of the probabilities of A and B? 2 7 c The probability of winning a game is a Explain how multiplying a fraction by a whole number can help you to work out the expected number of successes when an experiment is repeated. Give an example. b The probability of winning a game is 3 5 . What is the probability of not winning? . How many wins would you expect if you played the game 100 times? 3 A discount electrical store sells a brand of kettle with a probability of 0.32 that it contains a fault. Jenny buys two of these kettles for her work staff-room. 4 a Draw a tree diagram to show all the possible outcomes. b What is the probability that both kettles are faulty? c What is the probability that only one of the kettles contains a fault? a Draw a tree diagram to show the possible outcomes when a fair coin is tossed twice. Use your tree diagram to work out the probability of getting Heads both times. 5 b Carry out an experiment to estimate the experimental probability of getting two Heads when a coin is tossed twice. Decide how many trials you need in the experiment. Calculate the experimental probability of getting two Heads. c Write a short report explaining how you designed and carried out your experiment. Give your results and explain whether or not the experimental and theoretical probabilities are in agreement with each other. a Draw a tree diagram to show the possible outcomes when a fair coin is tossed three times. b What is the probability of getting i 3 Heads ii 2 Heads and 1 Tail (in any order)? EXTENSION LEVEL 6/7 6 At the ‘Hook-A-Duck’ stall at a school fete, children use a rod with a hook at the end to catch a duck floating in a large bowl of water. The underside of each duck is marked either S for star prize, W for win or L for lose. After a duck has been hooked it is always returned to the water before another duck is hooked. a For the trial ‘hooking-a-duck’, list the outcomes in the sample space. b For the trial described in a discuss whether or not you think the outcomes will be equally likely. In the bowl there is 1 duck marked S, 9 marked W and 2 marked L. c Write down the theoretical probability of the following events. i Winning the star prize iii Winning something v 7 ii Not winning the star prize iv Not winning any prize Just a win Another stall at the school fete has this board: PRIZE! 1 2 3 4 5 You throw a dice. You win a prize if your score is 5. You win a penny sweet if your score is an even number. 8 a List the outcomes in the sample space. b Write down the theoretical probability of the following events. i winning something iii not winning the prize ii not winning anything iv not winning a penny sweet Three fair tetrahedral dice X, Y and Z are thrown at the same time. The numbers on dice X are 1, 5, 5, 1 The numbers on dice Y are 4, 4, 4, 0 The numbers on dice Z are 2, 2, 6, 2 Copy and complete the tree diagram to show the different probabilities of the possible outcomes when these three dice are thrown. The scores shown on each dice are added together. a What is the highest possible score? b Work out the probability of getting the highest possible total score. 6