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Rock, paper, scissors Two player game Take turns and record the results TallyFrequency Player 1 Player 2 Draw

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Rock, paper, scissors Continue the table below showing ALL POSSIBLE OUTCOMES Player 1Player 2Result StoneScissorsPlayer 1 WINS

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Rock, paper, scissors Player 1Player 2Result RockScissorsPlayer 1 WINS Rock Draw RockPaperPlayer 2 WINS Scissors Draw ScissorsRockPlayer 2 WINS ScissorsPaperPlayer 1 WINS PaperScissorsPlayer 2 WINS PaperRockPlayer 1 WINS Paper Draw

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Rock, paper, scissors PLAYER 1 RockPaperScissors RockR, R Paper Scissors PLAYER 2

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Rock, paper, scissors Answer these questions in your books After 60 games, how many games should be a draw? Who is more likely to win? Explain why this is a fair game to play. Why are the frequencies not all the same? How can you even up the results for each player?

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Rock, paper, scissors After 60 games, how many games should be a draw? Who is more likely to win? Explain why this is a fair game to play. Why are the frequencies not all the same? How can you even up the results for each player? Noone As all possible outcomes are equally likely Theoretically, 20. Because this is just an experiment You should play many more games

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Rock, paper, scissors Calculating chance PROBABILITY = a measured chance of something happening. PROBABILITY =Favourable outcomes TOTAL number of outcomes Eg. The probability of winning at Rock, Paper, scissors is….

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Combining two events Here is another sample space diagram. What is it showing? Coin 1 Coin 2 HHHT THTT

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Combining two events Here is another sample space diagram. Complete the table. Spinner 1 RedBlueGreenYellow Spinner 2 Draw the two possible spinners

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Combining two events The score from two spinners are added together. Spinner Spinner 2 Complete this sample space diagram

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Combining two events Here are the answers… Spinner Spinner 2 Which scores are most likely to occur?

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Combining two events Two normal dice are rolled at the same time. Design a sample space diagram that can record the sum of the scores of the two dice.

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Combining two events DICE SCORE DICE SCORE 2

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Combining two events DICE SCORE DICE SCORE 2

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Expected frequency Expected frequency = probability x number of trials You can use the probability of an event to predict the number of times an outcome might happen. Example : Two people play the game Rock, Paper, Scissors, 300 times. Estimate the number of draws there will be. Out of 300 games, we would EXPECT = 100 DRAWS

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Questions Expected frequency = probability x number of trials 1. A dice is rolled 90 times. How many sixes would you expect? 2. A coin is flipped 80 times. How many heads would you expect? 3. Two out of three people prefer Summer than winter holidays. Out of 1000 people asked, how many prefer Summer holidays? 4. 1 out of every 8 people in England are vegetarian. How many vegetarians are there in england (Pop. England = 64 million)

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Relative frequency Relative frequency = estimated probability You can ESTIMATE probability using an experiment or historical information Example : A train is late 5 times in April. Estimate the probability that it will be late on the first day of May. Out of 30 days, 5 days the train was late. So P(Train is late) =

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Relative frequency A table shows the levels achieved by 100 students in a maths challenge competition. CertificateFrequency Gold14 Silver49 Bronze25 Pass12 Relative frequency = frequency of event total frequency Estimate the probability that : (a) A student achieves a gold certificate (b) A student achieves a pass (c) Which certificate are students most likely to achieve

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