Embedded Files
Lesson overview
Lesson overview
In this lesson you will:
explore the consquences of conditional probability
solve puzzles and look at game strategy when conditional probability is involved.
Activity 1 - Lick the frog
Activity 1 - Lick the frog
Think about this problem
Think about this problem
You’re stranded in a rainforest and you’ve eaten a poisonous mushroom. To save your life, you need an antidote excreted by a certain species of frog.
Unfortunately, only the female frog produces the antidote. The male and female look identical, but the male frog has a distinctive croak.
There is one frog in front of you but then you hear the distinctive male croak behind you and turn to see two frogs sitting behind you.
You don’t have time to go in both directions, which way do you go?
What are your chances of licking the right frog and being cured?
How can you go about solving this problem?
Public domain (CC0)
Task
Task
Watch the TEDEd video to explore the frog problem further.
Conditional Probability
Conditional Probability
In the Lick the frog problem, we saw an example of conditional probability. We knew that one of the two frogs had to be a male because we had heard its croak. This meant that we could eliminate some of the outcomes from our sample space, in this case, the outcome with two female frogs.
Keep this in mind as you complete the next few activities.
Can you solve the frog riddle? - Derek Abbott
Duration: 4:30
Activity 2 - The other child’s gender
Activity 2 - The other child’s gender
Can you solve the mystery?
Read the problem, the Other Child's gender from Transum.org, and see if you can help Detective Cluespot.
Click on the image to open the problem in a new tab.
Remember to draw a diagram to help you.
Activity 3 - Monty Hall problem
Activity 3 - Monty Hall problem
The Monty Hall problem is loosely based on a television show called Let’s make a deal.
You are on a game show and you are given the choice of 3 doors. Behind one door is a car, behind the other two doors are goats.
You pick a door. The host, who knows where the car is, will open one of the two remaining doors to reveal one of the goats.
You then have the option to stick to your original door, or to swap to the other unopened door.
Public domain (CC0)
Task
Task
Can you figure out what is the best strategy – to stick or switch?
Visit the Monty Hall simulation and complete the following activites.
Click on the image to open the simulation in a new tab.
First, choose the play tab and play a few games.
Then, click on the Simulate tab and run the simulation 100 times, choosing the strategy you would like to investigate first.
Record your results.
Run the simulation again but this time with the other strategy.
In your exercise book or folder:
Record the results you got from both strategies in terms of number of cars won and percentage of wins.
Answer the questions:
Did you get the same results with both strategies?
Should you stick or switch? What do the simulations suggest?
Explaining the solution
Explaining the solution
Try not to watch this video until you've come up with your own answer!
Watch the Monty Hall Problem - Numberphile video on YouTube for an explanation.
Activities too easy?
Activities too easy?
Bubblegum problem
Bubblegum problem
Complete the bubblegum problem from NZ Maths (PDF 175KB)
Can you extend this puzzle to find the number of items someone would have to buy for 4-colours, 5-colours etc?
Watch the Mathsplanations: Pigeonhole Principle and Sock Picking video on YouTube for an explanation of the Pigeon Hole Principle and to see how it applies to our Bubblegum problem.
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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