PROBABILITY

• Why can't you know beforehand what the outcomes in games of chance,like coin tossing, dice throwing or the Lotto, will be?

• In games of chance the outcomes are uncertain because the games arebased on random processes. Random processes mean that there is nopattern or system in the outcomes. That means that a player cannotcontrol the outcome. To think that you can, is to have an illusion ofcontrol.

• Do you think that the more you played the Lotto and studied the numbers,the better your chances of predicting the winning numbers?

• In games of chance the outcomes are independent events. That meansthat each Lotto number is as likely to come up now as in any time in thefuture. Your chance of predicting the winning numbers stays exactly thesame.

• The general rule for calculating the probability of an event (like picking acard, or throwing a number) where the chance of each outcome is thesame is:

p = n/t

(where p stands for probability, n for the number of favourable or desiredoutcomes making up the event, and t for the total number of possibleoutcomes.)

• What is the probability of throwing the number “4” with a die?

• What is the probability of winning the jackpot on a slot machine (assumingthat only one unique combination constitutes the jackpot)?

There is only a 1 in 52 521 875 chance of hitting the jackpot in any one play!

Grade 9 | Unit 9.3 | Page 9

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Roulette tables and roulette wheelsA roulette wheel has 37 numbers, from 0 through to 36.

Black and red numbers:

18 of these numbers are black; 18 of these numbers are red, and the “0”is green.

Even and odd numbers:

Also, 18 of these numbers are even (i.e. 2, 4, 6, 8, ... ,36), and 18 of thesenumbers are uneven or odd (i.e. 1, 3, 5, 7, 9, …,35). “0” is neither evennor odd.

• What is the probability that the roulette wheel will stop on an odd number?

(Answer: There are 18 odd numbers and 37 numbers in total. Thus theprobability of getting an odd number in roulette is 18/37.)

• How does being able to calculate the probability of the outcome and ofwinning help you make sensible decisions about getting involved in riskygambling?

Grade 9 | Unit 9.3 | Page 10

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