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Press Ctrl-APress Ctrl-A©G Dear 2010 – Not to be sold/Free to use

Counting OutcomesCounting OutcomesStage 6 - Year 11Stage 6 - Year 11

Applied Mathematic(Preliminary General 1)

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What occupations use Probability?

Funeral DirectorsEnvironmental health

Risk assessmentGovernment Service

Real Estate

Social Statistics

Risk ManagementActuarial Science

Farmers

Stock Clerks Source: http://www.xpmath.com/careers/topicsresult.php?subjectID=1&topicID=8

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The futility of Gambling!

1 in 9,765,625 for 1st Division

1 in 54,979,155 - 1st Prize

Probability of becoming a Problem Gamblergamblinghelponline.org.au/regaining-control/thinking-straight/what-are-the-odds.aspx

•If you gamble once or more a week on non-lottery types of gambling … 1 in 7.

•If you don't gamble … no chance at all.•If you only gamble occasionally … 1 in 50.

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Multistage Events – Multiplying Choices

When throwing a dice …there are 6 possible outcomes.

When throwing two die …there are 6 possibleoutcomes for the first die and ...there are 6 possible outcomesfor the second die.

Outcomes =6 x 6 = 36

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Multistage Events – Multiplying Choices

Outcomes =6 x 6 = 36

Dice 21 2 3 4 5 6

Dic

e 1

123456

111213141516212223242526313233343536414243444546515253545556616263646566

6

Multistage Events – Multiplying Choices

Outcomes =6! =6x5x4x3x2x1= 720

Arrangement of 6 people?

Factorial6

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Multistage Events – Multiplying Choices

Outcomes =5! =5x4x3x2x1 = 120

Arrangement of 5 people?

Factorial5

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Multistage Events – Multiplying Choices

Outcomes =4! =4x3x2x1 = 24

Arrangement of 4 people?

Factorial4

9

Multistage Events – Multiplying Choices

Outcomes =3! =3x2x1 = 6

Arrangement of 3 people?

Factorial3

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Multistage Events – Multiplying Choices

Outcomes =2! =2x1 = 2

Arrangement of 2 people?

Factorial2

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Multistage Events – Multiplying Choices

Outcomes =1! =1 = 1

Arrangement of 1 person?

Factorial1

12

Multistage Events – Listing Choices

Outcomes =2! =2x1 = 2

Arrangement of 2 letters?

AB

ABBA

Factorial2

13

Multistage Events – Listing Choices

Outcomes =3! =3x2x1 = 6

Arrangement of 3 letters?

ABC

ABC

ACBBACBCA

CABCBA

Factorial3

14

Multistage Events – Listing Choices

Outcomes =4! =4x3x2x1 = 24

Arrangement of 4 letters?

ABCD

ABCD

ABDCACBDACDBADBCADCB

BACDBADCBCADBCDABDACBDCA

CABDCADBCBADCBDACDABCDBA

DABCDACBDBACDBCADCABDCBA

Factorial4

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BCEDA

Multistage Events – Listing Choices

Outcomes =5! =5x4x3x2x1 = 120

Arrangement of 5 letters?

ABCDE

ABCDEABCEDABDCEABDECABECDABEDC

ACBDEACBEDACDBEACDEBACEBDACEDB

ADBCEADBECADCBEADCEBADEBCADECB

AEBCDAEBDCAECBDAECDBAEDBCAEDCB

BACDEBACEDBADCEBADECBAECDBAEDC

BCADEBCAEDBCDAEBCDEABCEAD

BDACEBDAECBDCAEBDCEABDEACBDECA

BEACDBEADCBECADBECDABEDACBEDCA

CABCDCABDCCADBECADEBCAEBCCAECB

CBADECBAEDCBDAECBDEACDABECDAEB

CDABE

Factorial5

CDAEBCDBAECDBEACDEABCDEBA

CEABDCEADBCEBADCEBDACEDABCEDBA

EABCDEABDCEACBDEACDBEADBCEADCB

EBACDEBADCEBCADEBCDAEBDACEBDCA

ECABDECADBECBADECBDAECABDECADB

EDABCEDACBEDBACEDBCAEDCABEDCBA

DABCEDABECDACBEDACEBDAEBCDAECB

DBACEDBAECDBCAEDBCEADBEACDBECA

DCABEDCAEBDCBAEDCBEADCEABDCEBA

DEABCDEACBDEBACDEBCADECABDECBA

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Multistage Events – Listing Choices

Outcomes =6! =6x5x4x3x2x1= 720

Arrangement of 6 letters?ABCDEF

Forget it.