switch doors? by jan bryson and andrew derer switch doors? photo courtesy of hatos-hall productions
TRANSCRIPT
Switch Switch Doors?Doors?
By Jan BrysonBy Jan Bryson
and Andrew Dererand Andrew Derer
Switch Doors?Switch Doors?
Photo Courtesy of Hatos-Hall Productions
Switch Doors?Switch Doors?
Photo Courtesy of Hatos-Hall Productions
How the game works:How the game works:• You get to choose a doorYou get to choose a door• But before you open it, let me But before you open it, let me
show you a door you didn’t show you a door you didn’t choosechoose
• Would you like to stick with your Would you like to stick with your door or door or switchswitch to the one door to the one door remaining?remaining?
Switch Doors?Switch Doors?
Today you will:Today you will:• Play a gamePlay a game• Have a chance to win a prizeHave a chance to win a prize• Figure out how to win a game Figure out how to win a game
more often than most peoplemore often than most people• Understand a problem that Understand a problem that still still
baffles mathematicians!baffles mathematicians!
Switch Doors?Switch Doors?
By the end of this lesson you By the end of this lesson you should know:should know:
• How experimental and theoretical How experimental and theoretical probability differprobability differ
• How to recognize theoretical and How to recognize theoretical and experimental probability in a math experimental probability in a math problemproblem
• Which probability to use to solve Which probability to use to solve probability problemsprobability problems
Switch Doors?Switch Doors?
1.1. ProbabilityProbability2.2. SimulationSimulation3.3. OutcomeOutcome4.4. TrialTrial5.5. EventEvent6.6. Experimental Experimental
ProbabilityProbability7.7. Theoretical Theoretical
ProbabilityProbability
Switch Switch Doors?Doors? Let’s Talk Let’s Talk
ProbabilityProbabilityDoes everyone know these terms?Does everyone know these terms?
• The likelihood of an event occurring
• Any process that yields a result or observation
• The result of a simulation
• One attempt or single simulation
• A specific outcome (example: a 3 on a die)
• The likelihood of an event happening based on repeated trials
• The likelihood of an event occurring based on expected results
Trying it outTrying it out
• Let’s try this a few times and see Let’s try this a few times and see what the results are…what the results are…
• We can keep track of them on We can keep track of them on the board.the board.
Switch Switch Doors?Doors?
1.1. State the problem clearlyState the problem clearly
2.2. Define the simple eventDefine the simple event
3.3. State the underlying assumptionsState the underlying assumptions
4.4. Select a model for each eventSelect a model for each event
5.5. Define and conduct a trialDefine and conduct a trial
6.6. Record the outcomeRecord the outcome
7.7. Repeat steps 5 & 6 a bunch of timesRepeat steps 5 & 6 a bunch of times
Switch Switch Doors?Doors? Creating a Creating a
SimulationSimulationLet’s see if we can play this game a Let’s see if we can play this game a bunch of times. First we need to:bunch of times. First we need to:
Keeping track of Keeping track of resultsresults
Door you selected Stick Switch Where's the Prize? Win/Loss
1 2 3 Door ___
Switch Switch Doors?Doors?
Circle the door you chooseDecide if you want to stick or switch and write it in.
Switch
Record where the prize was
2 Loss
Record the
outcome
This is how you keep track of each trialLet’s try a few together
• You get to choose a door (circle it You get to choose a door (circle it on your sheet).on your sheet).
• Flip the chip to decide if you will Flip the chip to decide if you will stick or switchstick or switch
• Roll the die to find out which door Roll the die to find out which door the prize is behind.the prize is behind.
• Record the resultsRecord the results
Switch Switch Doors?Doors?
Creating a Creating a SimulationSimulation
Keeping track of Keeping track of resultsresults
Door you selected Stick Switch Where's the Prize? Win/Loss
1 2 3 Door ___
Switch Switch Doors?Doors?
Switch 2 Loss
Trying it outTrying it out
Let’s look at this oLet’s look at this on the web!n the web!
Switch Switch Doors?Doors?
Seeing the Seeing the possibilitiespossibilities
Switch Switch Doors?Doors?
Here’s what the choices look likeHere’s what the choices look like
Pick a Door
Right
Wrong
Wrong
Only one of the three doors is right!
Stick
Switch
Stick
Switch
Stick
Switch
•Win!
•Lose
•Lose
•Win!
•Lose
•Win!
Sticking
Win Loss
Switching
Win Loss
Here’s where a door is revealed!
Seeing the Seeing the possibilitiespossibilities
Switch Switch Doors?Doors?
Sticking
Win Loss
Switching
Win Loss
2 out of 3 times you lose by sticking
2 out of 3 times you win with switching!
1.1. ProbabilityProbability2.2. SimulationSimulation3.3. OutcomeOutcome4.4. TrialTrial5.5. EventEvent6.6. Experimental Experimental
ProbabilityProbability7.7. Theoretical Theoretical
ProbabilityProbability
Switch Switch Doors?Doors?
Let’s Wrap it up!Let’s Wrap it up!
What is…What is…• The likelihood of an event occurring
• Any process that yields a result or observation
• The result of a simulation
• One attempt or single simulation
• A specific outcome (example: a 3 on a die)
• The likelihood of an event happening based on repeated trials
• The likelihood of an event occurring based on expected results
Switch Switch Doors?Doors?
Let’s Wrap it up!Let’s Wrap it up!
How do we make sure How do we make sure our experiment is at least our experiment is at least close to the theoretical close to the theoretical probability?probability?
Make sure we conduct lots of trials!
Switch Switch Doors?Doors?
Let’s Wrap it up!Let’s Wrap it up!
Do you know what to do Do you know what to do when they start up a new when they start up a new Let’s Make a DealLet’s Make a Deal show? show?Switch!
Questions?Questions?Thank youThank you