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

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

Rock, paper, scissors Player 1 Player 2 Result Rock Scissors Player 1 WINS Draw Paper Player 2 WINS

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

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?

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 likely After 60 games, how many games should be a draw? Theoretically, 20. Why are the frequencies not all the same? Because this is just an experiment How can you even up the results for each player? You should play many more games

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….

Combining two events Coin 1 Coin 2 HH HT TH TT Here is another sample space diagram. What is it showing? Coin 1 Coin 2 HH HT TH TT

Combining two events Spinner 1 Spinner 2 Here is another sample space diagram. Complete the table. Spinner 1 Red Blue Green Yellow 1 2 3 Spinner 2 Draw the two possible spinners

Combining two events Spinner 1 Spinner 2 The score from two spinners are added together. Spinner 1 1 2 3 4 Spinner 2 Complete this sample space diagram

Combining two events Spinner 1 Spinner 2 Here are the answers… Spinner 1 1 2 3 4 5 6 7 Spinner 2 Which scores are most likely to occur?

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.

Combining two events DICE SCORE 1 1 2 3 4 5 6 8 DICE SCORE 2

Combining two events DICE SCORE 1 1 2 3 4 5 6 7 8 9 10 11 12

Expected frequency = 100 DRAWS 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

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)

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) =

Relative frequency Certificate Frequency Gold 14 Silver 49 Bronze 25 Relative frequency = frequency of event total frequency A table shows the levels achieved by 100 students in a maths challenge competition . Estimate the probability that : Certificate Frequency Gold 14 Silver 49 Bronze 25 Pass 12 (a) A student achieves a gold certificate (b) A student achieves a pass (c) Which certificate are students most likely to achieve