GENERAL MATHEMATICS 3 WEEK 16 NOTES TERM 2

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1 GENERAL MATHEMATICS 3 WEEK 16 NOTES TERM 2 Calculating probability often involves large numbers. For example, in Lotto there are combinations of 6 numbers (in Lotto you choose 6 numbers out of 45 ie from the numbers 1 to 45), thus your chance of winning is very small. How big is a billion? That depends on whether you ask an Australian or an American! However, everyone agrees on the size of a million. In the decimal system one million is written with a 1 in the millions position. One million is a 1 in the millions position followed by zeros in the otherpositions; that is, Note that one million is a 1 followed by six zeros. Exercise Set 1 Q1. Match the numbers in parts a to h with the numerals listed in i to viii. (a) 8 million (i) (b) 8 thousand (ii) (c) 8 thousand 2 hundred (iii) (d) 82 thousand (iv) (e) 80 thousand 2 hundred (v) (f) 8 million 2 thousand (vi) (g) 8 million 2 hundred thousand (vii) (h) 8 million and 2 (viii)

2 Q2. Write these numbers in words. (a) (b) (c) (d) (e) (f) Have you ever seen a house price written as $1.2m or a salary advertised as $52K? The media often use abbreviations to make it easier for people to read and understand large numbers. A price followed by m means million, a price followed by b means billion and a price followed by K means thousand. Q3. Match the expressions in parts a to d with the numerals listed in I to iv. (a) $85K (i) $ (b) $8.5m (ii) $ (c) $850K (iii) $ (d) $85m (iv) $ Q4. Mario is selling his house. The price is $760K. Write the price in words. The symbols _, _ and = can be used to describe the relative size of numbers. Q5. Place one of the symbols _, _ or = between the pairs of numbers to make the statements true. (a) 3K 4000 (b) m (c) 1.3m (d) 3.4m 4000K (e) (f) 9K 9009 Q6. Are the following statements true or false? (a) > 7K (b) = (c) 5m 200 _> 25K (d) 3K 1000 = 3m (e) 8K 1000 = 9K (f) 6K - 4 = 2K

3 Gambling has been frowned upon by many people for a long time. More than 2000 years ago Aristotle wrote about the harmful effects of cheating and gambling. In particular, he was concerned by the use of unfair, biased dice. In 1661 the Government of England passed its first law against gambling and since then most other governments have passed laws against gambling in one form or another. However, many countries that otherwise disapprove of gambling allow lotteries to raise funds for such things as hospitals and education. Here are the results of a special charity lottery that had tickets. Exercise Set 2 Q1. What is the number of the ticket that won first prize? Q2. What is the value of the first prize? Q3. Just Wishing syndicate won first prize. What is a syndicate? Q4. What do the letters NFP after the Just Wishing syndicate mean?

4 Q5. Who won second prize? Q6. What do you think the winners of second prize plan to do with the money they won? Q6. Sarah Jones won third prize. What is Sarah s address? Q7. Chantelle has ticket What prize did she win? Q8. How much did each of these people win? (a) Alan, ticket (b) Ali, ticket (c) Trevor, ticket (d) Sanjay, ticket Q9. There were tickets sold in this special charity lottery. Matt bought one ticket. When he bought the ticket, what was the probability that he: (a) would win first prize? (b) wouldn t win first prize? Q10. How many prizes were there in the lottery? Q11. (a) How many losing tickets (that is tickets that didn t win any prize) were there in the lottery? (b) What percentage of the tickets in the lottery didn t win a prize? Q12. (a) Each ticket in the lottery cost $5. Find the total value of the tickets sold in the lottery. (b) Calculate the total value of the prize money. (c) What percentage of the value of the ticket sales was returned in prize money? (d) It cost $ to organise and administer the lottery. How much money did the lottery make for the charity?

5 In Australia, more gambling dollars are spent on horse racing than on any other gambling activity. Long before Australia s first official race meeting in 1810, people have been going to the races. As early as 4000 BC horse-drawn chariot races were a popular pastime. Australian gamblers can place a bet with bookmakers or the government controlled TAB. The government takes 15% of all money invested in races on the TAB. Bookmakers are commonly called bookies. Bookies consider many factors that affect a horse s chance of winning a race before they offer punters odds. The odds are a summary of the bookmaker s opinion of the chance the horse has of winning. When a bookie offers odds of 5 : 1, he is giving the horse one chance of winning to five chances of losing. It is another way of stating the horse has a probability of winning the race. Example Ronaldo placed a winning $10 bet on Hot Runner at 6 : 1. How much will he receive? Solution Ronaldo will receive 6 $10 plus his original bet of $10. The bookie will pay him $60 + $10, which is $70. Example Teresa placed a $9 winning bet at 7 : 2. How much will she receive from the bookie? Solution Odds of 7 : 2 means Teresa will win $7 for every $2 she invested. She will receive $9 plus her original $9 bet. She will receive $31.50 plus $9. This is a total of $ Exercise Set 3 Q1. Complete this table Q2. Jack places a $6 bet on Arabian Winds at 33 : 1. He is excited when it won. (a) Do you think the bookmaker thought Arabian Winds was going to win? Why or why not?

6 (b) How much money does Jack receive from the bookmaker? (c) How much does Jack win? Q3. Bookmakers had Devil s Lady starting at 2 : 1. Aaron places a $5 bet on Devil s Lady with the TAB and when it wins he received $22.50 from the TAB. How much more does he win with his TAB bet than he would have if he had placed the same bet with a bookie? Q4. When Swiftly won, Sarah received $22 from her bookmaker for her $2 bet. (a) How much did Sarah win? (b) What odds did the bookmaker give Swiftly of winning?