1. 1 Press Ctrl-A ©G Dear 2010 – Not to be sold/Free to use Counting Outcomes Stage 6 - Year 11 Applied Mathematic (Preliminary General 1)

2. 2 What occupations use Probability? Funeral Directors Environmental health Risk assessment Government Service Real Estate Social Statistics Risk Management Actuarial Science Farmers Stock Clerks Source: http://www.xpmath.com/careers/topicsresult.php?subjectID=1&topicID=8

3. 3 The futility of Gambling! 1 in 9,765,625 for 1 st Division 1 in 54,979,155 - 1 st Prize Probability of becoming a Problem Gambler gamblinghelponline.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.

4. 4 Multistage Events – Multiplying Choices When throwing a dice … there are 6 possible outcomes. When throwing two die … there are 6 possible outcomes for the first die and... there are 6 possible outcomes for the second die. Outcomes =6x 6 =36

5. 5 Multistage Events – Multiplying Choices Outcomes =6x 6 =36 Dice 2 1 2 3 4 5 6 Dice 1 123456123456 112121313141415151616 212122323242425252626 313132323343435353636 414142424343445454646 515152525353545455656 616162626363646465656

6. 6 Multistage Events – Multiplying Choices Outcomes =6! =6x5x4x3x2x1= 720 Arrangement of 6 people? Factorial 6

7. 7 Multistage Events – Multiplying Choices Outcomes =5! =5x4x3x2x1= 120 Arrangement of 5 people? Factorial 5

8. 8 Multistage Events – Multiplying Choices Outcomes =4! =4x3x2x1= 24 Arrangement of 4 people? Factorial 4

9. 9 Multistage Events – Multiplying Choices Outcomes =3! =3x2x1= 6 Arrangement of 3 people? Factorial 3

10. 10 Multistage Events – Multiplying Choices Outcomes =2! =2x1= 2 Arrangement of 2 people? Factorial 2

11. 11 Multistage Events – Multiplying Choices Outcomes =1! =1= 1 Arrangement of 1 person? Factorial 1

12. 12 Multistage Events – Listing Choices Outcomes =2! =2x1= 2 Arrangement of 2 letters? AB BA Factorial 2

13. 13 Multistage Events – Listing Choices Outcomes =3! =3x2x1= 6 Arrangement of 3 letters? ABC ACB BAC BCA CAB CBA Factorial 3

14. 14 Multistage Events – Listing Choices Outcomes =4! =4x3x2x1= 24 Arrangement of 4 letters? ABCD ABDC ACBD ACDB ADBC ADCB BACD BADC BCAD BCDA BDAC BDCA CABD CADB CBAD CBDA CDAB CDBA DABC DACB DBAC DBCA DCAB DCBA Factorial 4

15. 15 BCEDA Multistage Events – Listing Choices Outcomes =5! =5x4x3x2x1= 120 Arrangement of 5 letters? ABCDE ABCED ABDCE ABDEC ABECD ABEDC ACBDE ACBED ACDBE ACDEB ACEBD ACEDB ADBCE ADBEC ADCBE ADCEB ADEBC ADECB AEBCD AEBDC AECBD AECDB AEDBC AEDCB BACDE BACED BADCE BADEC BAECD BAEDC BCADE BCAED BCDAE BCDEA BCEAD BDACE BDAEC BDCAE BDCEA BDEAC BDECA BEACD BEADC BECAD BECDA BEDAC BEDCA CABCD CABDC CADBE CADEB CAEBC CAECB CBADE CBAED CBDAE CBDEA CDABE CDAEB CDABE Factorial 5 CDAEB CDBAE CDBEA CDEAB CDEBA CEABD CEADB CEBAD CEBDA CEDAB CEDBA EABCD EABDC EACBD EACDB EADBC EADCB EBACD EBADC EBCAD EBCDA EBDAC EBDCA ECABD ECADB ECBAD ECBDA ECABD ECADB EDABC EDACB EDBAC EDBCA EDCAB EDCBA DABCE DABEC DACBE DACEB DAEBC DAECB DBACE DBAEC DBCAE DBCEA DBEAC DBECA DCABE DCAEB DCBAE DCBEA DCEAB DCEBA DEABC DEACB DEBAC DEBCA DECAB DECBA

16. 16 Multistage Events – Listing Choices Outcomes =6! =6x5x4x3x2x1= 720 Arrangement of 6 letters? ABCDEF Forget it.