STAT175 Lecture 1 PDF

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Lecture 1...

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STAT175 Lecture 1 Lotto & Lotteries Oz Lotto - $1.10 per game - 7 numbers selected from 1 to 45 - 7 numbers and 2 supplementary drawn - 60 % is allocated to prizes and 40 % goes back to game maker.

PERMUTATIONS AND COMBINATIONS Permutations is the number ways of selecting something without replacement when order is important

Combinations are the number of ways of selecting objects when order does not matter.

Division 1 prize - Order not important (COMBINATIONS) - n = 45 , r = 7 - 45C7 = 45!/7!(38!) = 45379620 - Therefore the probability is 0.000000022 (1 in 45 million) Division 7 Prize - 3 main winning numbers & a supplementary o Could be 3 main, 2 supp, 2 losing o OR 3 main, 1 supp, 3 losing

= 22050

= 499800 o Therefore total number of winning outcomes = 521850 o Divide number of div 7 outcomes by the total number of 7 number outcomes  521850/45379620 = 0.0115 Expected Winnings (ozlotto) - Prize pool is determined by the gross pool of money invested in the games o Operator keeps 40% & Prize pool is 60% -

Number of $1 games = n Gross pool = $n Dividend pool = $0.6n o (using these values the expected winnings of a ticket does not actually depend on how many tickets are bought)

Example Expected winnings (DIVISION 7) - Dividend pool = share awarded to div 7 x total dividend pool o Div. pool = 0.269 x 0.6n = 0.1614n - Probability of winning div 7 (From above) To find exp. winnings o 0.0115 - Find share of div pool o Therefore number of winners = 0.0115n - Find expected number of - Expected prize value winners o 0.1614n/0.0115n = $14.03 - Div. pool / winners

NSW Lotto - 6 numbers selected from 45 (must play at least 6 games) o 6 winning numbers 2 supplementary - Draws 3 times a week - Winning % vary on different draws...