Embedded Files
Lesson overview
Lesson overview
In this lesson you will:
learn to represent sample spaces
think about probability in relation to the fairness of games
use tree diagrams to solve probability problems.
Activity 1 - The last banana
Activity 1 - The last banana
Think about this problem
Think about this problem
You and a friend are stuck on a remote island and you only have one banana left. You decide to play a game to decide who will get to eat the banana.
Two dice are rolled and if the highest number is a one, two, three, or four you win.
If the highest number is a five or six your friend wins.
Who has the best probability of winning the game? Explain your reasoning using diagrams or maths.
How can you go about solving this?
Task
Task
Watch the TEDEd video to explore the banana problem further.
Complete the following questions in your exercise book or folder.
Record the sample space as shown in the video and then highlight the combinations where 1 is the highest, and then use a different colour to highlight the combinations where 2 is the highest etc
Work out the probability of each number being the highest. Order these from largest to smallest.
How could you alter the game to make it fair?
The last banana: A thought experiment in probability - Leonardo Barichello
Duration: 4:09
Activity 2 - Representing sample spaces of multi-stage events
Activity 2 - Representing sample spaces of multi-stage events
Definition:
A sample space is what we call all the possible outcomes of an experiment or action.
For example if you are choosing one card from a full deck the sample space is all 52 possible cards in a deck.
Task 1
Task 1
Before we calculate the probability of an event occurring, it is important to list the sample space to ensure we have considered all the different possible outcomes.
In this interactive you explore an example of a probability experiment and look at how you can represent its sample space.
Don't forget to export text at the end so you can share your answer to the last question with your teacher.
Let's apply what we just learned about sample spaces to a problem.
Task 2 - Spiky spheres
Task 2 - Spiky spheres
Nine spiky spheres are put in a bag. Some are red and some are yellow.
You pick a sphere, note the colour, put it back in the bag and pick another.
Can the probability of obtaining two of the same colour be close to a ½?
Complete this activity using the Spiky spheres Google Doc.
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.
Activity 3 - Rock, paper, scissors
Activity 3 - Rock, paper, scissors
Play Rock, paper, scissors against an AI.
Click on the image to open the website in a new tab.
While you play try to figure out if this is truly a fair game?
Complete the following questions in your exercise book or folder:
Draw a diagram in your workbook to show all of the different possible combinations. Highlight the combinations in which you win.
Calculate:
P(Player 1 wins)=
P(Player 2 wins) =
P(tie) =
How do these probabilities compare with those from when you played the computer? Are the same? Why/Why not?
Read the explanation of what the computer is thinking. What is your strategy when you play? If you play paper and lose, what will your next move be?
Play a few rounds with a friend or family member. Can you detect their strategy and use it against them.
Activity 4 - Tree diagram practice
Activity 4 - Tree diagram practice
Complete the following questions in your exercise book or folder:
A family decides to have 3 children.
Draw a tree diagram to show all of the outcomes.
What is the probability of having 2 boys?
What is the probability of having at least one girl?
A 4-sided die, numbered 1, 2, 3 and 4, is rolled twice.
Draw a tree diagram to show all possible outcomes
What is the P(two odd numbers in a row)?
What is the P(one odd and one even number)?
What is the P(sum of the two numbers is a square)?
Look at your tree diagram again. If the 4 sided dice was actually rolled 3 times, how many different outcomes would there be? Can you explain the pattern?
Public domain (CC0)
A 6-sided die is rolled.
If the number is odd, a 4 sided die is then rolled.
If the number is even, a spinner numbered 1 – 3 is spun.
Draw a tree diagram to show all outcomes.
What is P(two even numbers)?
What is P(two odd numbers)?
What is the P(the spinner gets spun)?
Imagine you were only asked to find the P(two even numbers). Can you re-draw your tree diagram to make it more efficient? I.e. with fewer branches.
Activities too easy?
Activities too easy?
Task 1
Task 1
Watch Sheldon from Big Bang Theory explain the game Rock, Paper, Scissors, Lizard, Spock on YouTube.
The game works this way:
"Scissors cuts paper, paper covers rock, rock crushes lizard, lizard poisons Spock, Spock smashes scissors, scissors decapitates lizard, lizard eats paper, paper disproves Spock, Spock vaporizes rock, and as it always has, rock crushes scissors."
Complete the following questions on this game in your exercise book or folder:
Draw a diagram to show the combinations in this game.
Circle the combinations in which you win.
Determine the probability of:
P(Player 1 wins) =
P(Player 2 wins) =
P(tie) =
How does this game compare to the original game? Is it fair? Is it easier or harder to win?
Task 2
Task 2
Visit the Tree Diagrams page on the the Transum.org website and complete the interactive problems.
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
Page updated
Report abuse