The bookmakers’ odds are:

1. The Big Match Cardiff City v Swansea City at The Cardiff City Stadium The bookmakers’ odds are: Home win: 9-5 Draw: 12-5 Away win: 7-5 What is the probability of each outcome, according to this information?

2. The Big Match Cardiff City v Swansea City The bookmakers’ odds are: Home win: 9-5 Draw: 12-5 Away win: 7-5 Which of the following statements is correct? State the letter of your answer. The probability of each result is:

3. How should you check if your working is correct? What do you notice about your answers? Why could this be?

4. Why should the three probabilities add up to 1? • Why don’t they add up to 1 exactly? • What percentage error is there? • What could explain this percentage?

5. Information sheet The football pages of some Saturday morning newspapers sometimes show the betting odds of a home win, draw or away win for each match in the Premier League that weekend. • For odds of 2-1, if you place a £1 bet, you will receive £2 for winning, but your £1 stake will also be returned, giving you a total of £3. • For odds of 9-5, your £1 is split into 5 parts (each 20p), and if you win you get 9 parts back (9 × 20p = £1.80), but your £1 stake will also be returned, giving you a total of £2.80. • For odds of 1-2, your £1 is split into 2 parts (each 50p), and if you win you get 1 part back (50p) plus your original £1, totalling £1.50. • If you lose, you get nothing, usually.

6. Other Premiership matches • Use the information to work out the probabilities of the three different outcomes from 3 other matches in the Premiership. What do you notice about the sums of the probabilities for each match? • If you put £1 on each outcome for each match, do you win or lose overall?

7. Other Premiership matches • What are the probabilities for each outcome for each match, and what is the sum of these match probabilities?