2 Rock, paper, scissors Tally Frequency Player 1 Player 2 Draw Two player gameTake turns and record the resultsTallyFrequencyPlayer 1Player 2Draw
3 Rock, paper, scissors Player 1 Player 2 Result Stone Scissors Continue the table below showing ALL POSSIBLE OUTCOMESPlayer 1Player 2ResultStoneScissorsPlayer 1 WINS
4 Rock, paper, scissors Player 1 Player 2 Result Rock Scissors Player 1 WINSDrawPaperPlayer 2 WINS
5 Rock, paper, scissorsPLAYER 1RockPaperScissorsR, RPLAYER 2
6 Rock, paper, scissors Answer these questions in your books Who is more likely to win?Explain why this is a fair game to play.After 60 games, how many games should be a draw?Why are the frequencies not all the same?How can you even up the results for each player?
7 Rock, paper, scissors Who is more likely to win? Noone Explain why this is a fair game to play.As all possible outcomes are equally likelyAfter 60 games, how many games should be a draw?Theoretically, 20.Why are the frequencies not all the same?Because this is just an experimentHow can you even up the results for each player?You should play many more games
8 Rock, paper, scissors Calculating chance PROBABILITY = a measured chance of something happening.PROBABILITY = Favourable outcomesTOTAL number of outcomesEg. The probability of winning at Rock, Paper, scissors is….
9 Combining two events Coin 1 Coin 2 HH HT TH TT Here is another sample space diagram. What is it showing?Coin 1Coin 2HHHTTHTT
10 Combining two events Spinner 1 Spinner 2 Here is another sample space diagram. Complete the table.Spinner 1RedBlueGreenYellow123Spinner 2Draw the two possible spinners
11 Combining two events Spinner 1 Spinner 2 The score from two spinners are added together.Spinner 11234Spinner 2Complete this sample space diagram
12 Combining two events Spinner 1 Spinner 2 Here are the answers…Spinner 11234567Spinner 2Which scores are most likely to occur?
13 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.
14 Combining two eventsDICE SCORE 11234568DICE SCORE 2
16 Expected frequency = 100 DRAWS Expected frequency = probability x number of trialsYou 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
17 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)
18 Relative frequency Relative frequency = estimated probability You can ESTIMATE probability using an experiment or historical informationExample : 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.SoP(Train is late) =
19 Relative frequency Certificate Frequency Gold 14 Silver 49 Bronze 25 Relative frequency = frequency of eventtotal frequencyA table shows the levels achieved by 100 students in a maths challenge competition .Estimate the probability that :CertificateFrequencyGold14Silver49Bronze25Pass12(a) A student achieves a gold certificate(b) A student achieves a pass(c) Which certificate are students most likely to achieve