1. Horse race © www.teachitmaths.co.uk 2012162881

2. Horse race: rules 1.Each player chooses a horse and puts it into a stall. Write your name next to the stall you pick. 2.Throw the two dice and add the scores together. The horse in that stall jumps forward one space. 3.The winner is the horse who is first past the post! Play in groups of up to 11 people with two 6-sided dice. © www.teachitmaths.co.uk 2012162882

3. Horse race: outcomes Discuss: Does each horse have an equal chance of winning? If you play the game a few times, is there a horse you would expect to win more often? How can you show which horse will be the best to pick? Who won the race? Is this game fair? © www.teachitmaths.co.uk 2012162883

4. Horse race: outcomes Complete this sample space diagram to explore all of the possible outcomes of rolling two dice. + Dice 1 123456 Dice 2 1 2 3 4 5 6 © www.teachitmaths.co.uk 2012162884

5. Horse race: outcomes Use your sample space diagram to discuss which horses have an equally likely chance of winning. + Dice 1 123456 Dice 2 1234567 2345678 3456789 45678910 56789 11 6789101112 © www.teachitmaths.co.uk 2012162885

6. Horse race: probabilities How many outcomes are there in total? 36 How many ways are there of getting a score of 5? 4 What is the probability of scoring 5? 4 / 36 = 1 / 9 + Dice 1 123456 Dice 2 1234567 2345678 3456789 45678910 56789 11 6789101112 © www.teachitmaths.co.uk 2012162886

7. Horse race: probabilities 1.P(score is 2) 2.P(score is 6) 3.P(score is 7) 4.P(score is 10) 5.P(score is 4 or less) 6.P(score is greater than 4) 7.P(score is an even number) 8.P(score is not 8) Use your sample space diagram to find these probabilities: 1 / 36 5 / 36 3 / 36 = 1 / 12 30 / 36 = 5 / 6 6 / 36 = 1 / 6 18 / 36 = 1 / 2 31 / 36 6 / 36 = 1 / 6 © www.teachitmaths.co.uk 2012162887

8. Horse race: expected outcomes 1.Which horse is most likely to win the race? 2.Will you definitely win if you pick this horse? 3.If the race was 10 squares long and all 11 horses were racing... 1.... what is the maximum number of throws before there was a winner? 2.... what is the minimum number of throws before there was a winner? 4.What is the probability that horse 7 wins after ten throws? 5.What is the probability that horse 2 wins after ten throws? 7 no 10 11 × 9 + 1 = 100 ( 1 / 6 ) 10 = 1 / 60,466,176 ( 1 / 36 ) 10 = 1 / 3,656,158,440,000,000 © www.teachitmaths.co.uk 2012162888