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**Simple probability and independent events**

1 of 38 © Boardworks Ltd 2014

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Horse race game Press the dice to roll them. The horse with that total score then moves forward one square. The winning horse is the first one to cross the finish line. Ask the class to discuss which horse they think will win. Play the game several times. 2

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**Horse race game Which horse has the best chance of winning?**

Are there any horses that can’t win? Which horses are unlikely to win and why? What combinations of scores give a total of 8? How many combinations produce a total of 12? Horse race © Cheryl Ann Quigley, Shutterstock.com How would the game change if you used ten-sided dice? 3

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**Combinations on two dice**

Horse Combinations Ways Probability 1 1 2 1,1 1 36 2 1 3 1,2 2,1 2 = 36 18 3 1 4 1,3 3,1 2,2 3 = 36 12 4 1 5 1,4 4,1 2,3 3,2 4 = 36 9 6 1,5 5,1 2,4 4,2 3,3 5 5 36 6 1 7 1,6 6,1 2,5 5,2 3,4 4,3 6 = 36 6 8 2,6 6,2 3,5 5,3 4,4 5 5 Ask pupils for their results. Before beginning the last column, ask “How many combinations are there altogether?” and “What will the probabilities be out of?” Ask pupils to cancel down the fractions when appropriate. The fractions have been left with denominators of 36 to demonstrate the symmetry. 36 4 1 9 3,6 3,6 4,5 5,4 4 = 36 9 10 4,6 4,6 5,5 3 3 1 = 36 12 11 5,6 6,5 2 2 1 = 36 18 1 12 6,6 1 36 4

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Sample space diagrams Another way of displaying all the outcomes from throwing two dice is a sample space diagram. Second dice Fill in the rest of the cells in the table. + 1 2 3 4 5 6 1 3 Colour in all the twos one colour, the threes another colour and so on. 2 First dice 3 8 4 5 What patterns do you notice in the table? 6 9 5

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**Now make up your own questions!**

Sample space diagrams Second dice What is the probability of getting a total more than 5? What is the probability of getting a total less than 10? What is the probability of getting a total that is a square number? What is the probability of getting an even total? What is the probability of getting an odd total? What is the probability of getting a total less than 13? + 1 2 3 4 5 6 1 2 2 3 3 4 4 5 5 6 6 7 7 2 3 3 4 4 5 5 6 6 7 7 8 8 First dice 3 4 4 5 5 6 6 7 7 8 8 9 9 4 5 5 6 6 7 7 8 8 9 9 10 10 5 6 6 7 7 8 8 9 9 10 10 11 11 6 7 7 8 8 9 9 10 10 11 11 12 12 Now make up your own questions! 6

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**Horse game with 8-sided dice**

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Sample space diagrams A coin and a ten-sided dice are thrown and the outcomes recorded in the two-way table below. Dice 1 2 3 4 5 6 7 8 9 10 H 1,H 2,H 3,H 4,H 5,H 6,H 7,H 8,H 9,H 10,H Coin T 1,T 2,T 3,T 4,T 5,T 6,T 7,T 8,T 9,T 10,T How many outcomes are there? What is the probability of heads and an even number? What is the probability of tails and a square number? Make up a fair game and an unfair game based on scoring points from outcomes in the table. 8

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