Multiple Events

1. Multiple Events

2. Multiple Events Multiple events are where two or more events happen together. e.g. rolling 2 die tossing a coin and rolling a die taking two discs out of a box the gender of 3 children in a family

3. Finding Probabilities For Multiple Events A common method for finding probabilities in multiple events is to list the sample space. There are 3 methods that you can use to list a sample space. Method 1: Use common sense Method 2: Use a table Method 3: Use a tree diagram

4. Multiple Events Notes: Instead of notes to copy into your book, we are going to work through 6 questions and then you can ask for extra notes if you feel that you need them. Remember to stick the example sheet into your workbook.

5. Listing a Sample SpacesExample 1 (a) List the sample space for tossing 2 coins Common Sense Table Tree Diagram HH HT TH TT

6. Listing a Sample SpacesExample 1 (a) List the sample space for tossing 2 coins Common Sense Table Tree Diagram Coin 2 HH HT TH TT Coin 1

7. TH 2nd Coin 1st Coin Sample Space T T T H H H TT HH HT Listing a Sample SpacesExample 1 (a) List the sample space for tossing 2 coins Common Sense Table Tree Diagram Coin 2 HH HT TH TT Coin 1

8. TH 2nd Coin 1st Coin Sample Space T T T H H H TT HH HT Listing a Sample SpacesExample 1 (a) List the sample space for tossing 2 coins Common Sense Table Tree Diagram Coin 2 HH HT TH TT Coin 1

9. TH 2nd Coin 1st Coin Sample Space T H H T T H TT HH HT Listing a Sample SpacesExample 1 (a) List the sample space for tossing 2 coins Common Sense Table Tree Diagram Coin 2 HH HT TH TT Coin 1 Which method would you be most likely to use if asked this question? Write your preferred method on the notes sheet.

10. TH 2nd Coin 1st Coin Sample Space T T H H T H TT HH HT Listing a Sample SpacesExample 1 Take 1 minute to answer parts 1b) 1c) & 1d) using your chosen sample space. Common Sense Table Tree Diagram Coin 2 HH HT TH TT Coin 1

11. TH 2nd Coin 1st Coin Sample Space H T H H T T TT HH HT Listing a Sample SpacesExample 1 (b) What is the probability of 2 heads? Pr(2 heads) = Coin 2 HH HT TH TT Coin 1

12. TH 2nd Coin 1st Coin Sample Space H T H H T T TT HH HT Listing a Sample SpacesExample 1 (c) What is the probability of no tails? Pr(no tails) = Coin 2 HH HT TH TT Coin 1

13. TH 2nd Coin 1st Coin Sample Space H T H H T T TT HH HT Listing a Sample SpacesExample 1 (d) What is the probability of head & tail in any order? Pr(2 heads) = Coin 2 HH HT TH TT Coin 1

14. 3rd Child 2nd Child 1st Child Sample Space GGB GGG BBB GBB BGB B B B G B B G G B G B G G G BBG BGG GBG Listing a Sample SpacesExample 2 Which method would you be most likely to use if asked this question? Write your preferred method on the notes sheet. (a) List the sample space for the gender of 3 children Common Sense Tree Diagram BBB BBG BGB BGG GBB GBG GGB GGG

15. 3rd Child 2nd Child 1st Child Sample Space GGB GGG BBB GBB BGB B B B G G B B G G B G G B G BBG BGG GBG Listing a Sample SpacesExample 2 (a) List the sample space for the gender of 3 children Take 1 minute to answer parts 2b) 2c) & 2d) using your chosen sample space. Common Sense Tree Diagram BBB BBG BGB BGG GBB GBG GGB GGG

16. 3rd Child 2nd Child 1st Child Sample Space GGB GGG GBB BGB BBB G B G B G B B B G B G G B G BGG BBG GBG Listing a Sample SpacesExample 2 (b) What is the probability that the last two children are girls? Pr(last 2 are girls) = BBB BBG BGB BGG GBB GBG GGB GGG

17. 3rd Child 2nd Child 1st Child Sample Space GGB GGG GBB BGB BBB G B G B G B B B G B G G B G BGG BBG GBG Listing a Sample SpacesExample 2 (c) What is the probability of no boys? Pr(no boys) = BBB BBG BGB BGG GBB GBG GGB GGG

18. 3rd Child 2nd Child 1st Child Sample Space GGB GGG GBB BGB BBB G B G B G B B B G B G G B G BGG BBG GBG Listing a Sample SpacesExample 2 (d) What is the probability of the sex of each successive child being different (e.g. BGB or GBG) ? Pr(no boys) = BBB BBG BGB BGG GBB GBG GGB GGG

19. Listing a Sample SpacesExample 3 & 4 Explore examples 3 & 4 by considering what we discussed in examples 1 & 2.

20. Listing a Sample SpacesSample Space For Example 3 Spinner 2 Spinner 1

21. 3rd Light 2nd Light 1st Light Sample Space RRG RRR GGG RGG GRG G G R R G R G R R G G R R G RGR GGR GRR Listing a Sample Spaces Sample Space For Example 4

22. R Y W Listing a Sample SpacesIntroduction To Example 5 Two marbles are taken out of the box opposite without replacement. List the sample space for this situation. Common Sense YW , YR RY , RW WY , WR

23. Y W R YW RW WR YR RY WY Listing a Sample SpacesIntroduction To Example 5 Two marbles are taken out of the box opposite without replacement. List the sample space for this situation. Common Sense YW , YR RY , RW WY , WR Tree Diagram 2nd marble 1st marble Sample Space R W Y W Which method do you prefer? R Y W Use this example to answer the questions in Example 5 Y R

24. W Y R G Y W G Y G R W R R W Listing a Sample SpacesExample 5 2nd marble 1st marble Sample Space YW YR Y G YG Y WY WR W WG RY RW R RG GY GW G GR

25. Y Y W Y W Probabilities Listing a Sample Spaces Introduction To Example 6 (Thinking Question) Two marbles are taken out of the box opposite without replacement. List the sample space for this situation. 2nd Disk 1st Disk Sample Space W WW W Y WY W YW Y Y YY

26. Y W Y W W W R Listing a Sample Spaces Example 6 (Thinking Question) Two marbles are taken out of the box opposite without replacement. List the sample space for this situation. Look at the Board

27. Multiple Events Practice Exercise Complete the Multiple Events Practice Exercise as a class task or homework.