Embedded Files
Lesson overview
Lesson overview
In this lesson you will:
practise deciding if events are dependent or independent
draw tree diagrams and calculate probabilities
graph probabilities to discover patterns and predict strategies.
Activity 1 - What is an independent event?
Activity 1 - What is an independent event?
Task 1
Task 1
Watch the video, Probability of Independent and Dependent Events (6.2), to view an explanation of the difference between independent and dependent events.
Probability of Independent and Dependent Events (6.2)
Duration: 6:43
Task 2
Task 2
Visit the Tree Diagrams page on Transum.org.
Click on the image link to open the activity in a new tab.
Complete the Level 1 activities to practice drawing tree diagrams and calculating probabilities.
Be sure to read the questions carefully to decide if they are dependent or independent events.
Note: If you already completed Level 1 as an extension activity complete Level 2, drawing the tree diagrams in your exercise book or folder.
Activity 2 - Apwerte
Activity 2 - Apwerte
Background
Background
Apwerte is bowling-type games using rounded stones that was played near Warrina in central Australia. Another, similar rolling game was observed being played on a river flat at Goondiwindi in Queensland.
Men used to roll the stones as far as they could to show their strength, or roll them towards other stones or between markers to demonstrate their accuracy in bowling.
Apwerte means ‘stone’ in the language of the Eastern Arrerente people of central Australia.
Note: This information is adapted from apwerte by the Australian Sports Commission (PDF 112KB).
Task
Task
Kirra and Jedda decide to play a variation of apwerte where they will roll tennis balls between two cone markers. They will score a point for each time the ball rolls through the cones without touching them.
After playing for a while, the girls calculate that Kirra has an 80% chance of successfully rolling her ball through the cones, while Jedda is slightly less accurate, with a 78% chance.
The girls decide to have 5 turns each.
Use the information about Kirra and Jedda's game to answer the following questions in your exercise book or folder:
Draw a tree diagram for each girl, showing the outcomes for their 5 turns. Make sure you label each branch with the correct probability.
What is the probability that they score 5 points?
What is the probability that they score 0 points?
What is the probability that they score 3 points?
Activity 3 - Which team will win?
Activity 3 - Which team will win?
Every weekend, Team B and Team Y play each other at 2 goal football. They play until a total of two goals have been scored.
Task
Task
Use the embedded NRICH website to complete the activity.
Start by pressing the Play 36 button to generate some data.
Once the data is generated you can use the scroll bar to see the results for each of the 36 matches.
Use the results to complete the following activites in your exercise book or folder.
Part 1
Calculate the probabilities from your spinner data:
P(team B wins) =
P(team Y wins) =
P(YB draw) =
P(BY draw) =
Draw a tree diagram to represent the different outcomes for the two goals. Label your tree diagram with the probability of each team scoring.
Part 2
Calculate the probabilities from Part 1 again but this time, using your tree diagram.
How do they compare to the probabilities from Part 1?
Are they the same?
Why/Why not?
Alter the probabilities for each goal (they do not have to be the same) and repeat Parts 1 and 2.
Activity 4 - Greedy pig
Activity 4 - Greedy pig
Information on the game
Information on the game
Greedy pig is a game where one person rolls a die and the other players have a chance to score based on the result of the dice.
Players can lose their score if they get too greedy so they have to decide whether to stand up or sit down before each dice roll.
If a player sits down before the throw, they get to keep their score and record it.
The dice is rolled over and over until every player is sitting down or a 1 is thrown.
If the number rolled is:
2 to 6, then the players add the amount thrown to their score, and the next roll is taken.
1, then the players who are still standing lose their score and go back to zero and the game ends.
Task
Task
Use this Google Doc to complete the task.
Click on the button to open a new tab and view the Google Doc.
Click on the Use Template button to create a copy for you to edit.
Activities too easy?
Activities too easy?
Read the following story and decide what Janice should do. (Draw a diagram to help you decide.)
Janice has an after school job, for an hour each school day. To get to the job, she parks her moped on a P60 space on the street outside. She doesn't use the nearby parking building which charges $3 for the first two hours of parking.
Using the P60 is usually fine, but she does get held up at work 2 out of every 5 days and so overstays the allowed 60 minutes on those days. There is a 25% chance on any given day, that parking wardens are around and will write a $20 fine for cars overstaying their park.
Should Janice keep risking the P60 parking, or would she save money by using the parking building?
Handing in your work
Handing in your work
Don't forget to hand in the work you completed today!
Your teacher will have told you to do one of the following:
Upload any digital documents you created and any photos you took of your written work to your Learning Management system (MS Teams, Google Classroom for example).
Email any digital documents you created and any photos you took of your written work to your teacher.
Make sure you keep any hand written work you did in your exercise book or folder as your teacher may need to see these when you are back in class.
Student reflection
Student reflection
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