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**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**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**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.**Listing a Sample SpacesExample 1**(a) List the sample space for tossing 2 coins Common Sense Table Tree Diagram HH HT TH TT**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**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**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**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.**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**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**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**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**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**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**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**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**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**Listing a Sample SpacesExample 3 & 4**Explore examples 3 & 4 by considering what we discussed in examples 1 & 2.**Listing a Sample SpacesSample Space For Example 3**Spinner 2 Spinner 1**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**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**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**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**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**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**Multiple Events Practice Exercise**Complete the Multiple Events Practice Exercise as a class task or homework.