Switch Doors? By Jan Bryson and Andrew Derer

Switch Doors? Photo Courtesy of Hatos-Hall Productions

Switch Doors? Photo Courtesy of Hatos-Hall Productions

How the game works: You get to choose a doorYou get to choose a door But before you open it, let me show you a door you didn’t chooseBut before you open it, let me show you a door you didn’t choose Would you like to stick with your door or switch to the one door remaining?Would you like to stick with your door or switch to the one door remaining? Switch Doors?

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 more often than most peopleFigure out how to win a game more often than most people Understand a problem that still baffles mathematicians!Understand a problem that still baffles mathematicians! Switch Doors?

By the end of this lesson you should know: How experimental and theoretical probability differHow experimental and theoretical probability differ How to recognize theoretical and experimental probability in a math problemHow to recognize theoretical and experimental probability in a math problem Which probability to use to solve probability problemsWhich probability to use to solve probability problems Switch Doors?

1.Probability 2.Simulation 3.Outcome 4.Trial 5.Event 6.Experimental Probability 7.Theoretical Probability Switch Doors? Let’s Talk Probability 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 out Let’sLet’s try this a few times and see what the results are… WeWe can keep track of them on the board. Switch Doors?

1.State the problem clearly 2.Define the simple event 3.State the underlying assumptions 4.Select a model for each event 5.Define and conduct a trial 6.Record the outcome 7.Repeat steps 5 & 6 a bunch of times Switch Doors? Creating a Simulation Let’s see if we can play this game a bunch of times. First we need to:

Keeping track of results Dooryou selected StickSwitch Where'sthePrize? Win/Loss 123 Door ___ Switch Doors? Circle the door you choose Decide if you want to stick or switch and write it in. Switch Record where the prize was 2Loss Record the outcome This is how you keep track of each trial Let’s try a few together

You get to choose a door (circle it on your sheet).You get to choose a door (circle it on your sheet). Flip the chip to decide if you will stick or switchFlip the chip to decide if you will stick or switch Roll the die to find out which door the prize is behind.Roll the die to find out which door the prize is behind. Record the resultsRecord the results Switch Doors? Creating a Simulation

Keeping track of results Dooryou selected StickSwitch Where'sthePrize? Win/Loss 123 Door ___ Switch Doors? Switch2Loss

Trying it out Let’s look at this on the web! Switch Doors?

Seeing the possibilities Switch Doors? Here’s what the choices look like Pick a Door Right Wrong Only one of the three doors is right! Stick Switch Stick Switch Stick Switch Win! Lose Win! Lose Win! Sticking Win Loss Switching Win Loss Here’s where a door is revealed!

Seeing the possibilities Switch 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.Probability 2.Simulation 3.Outcome 4.Trial 5.Event 6.Experimental Probability 7.Theoretical Probability Switch Doors? Let’s Wrap it up! 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 Doors? Let’s Wrap it up! How do we make sure our experiment is at least close to the theoretical probability? Make sure we conduct lots of trials!

Switch Doors? Let’s Wrap it up! Do you know what to do when they start up a new Let’s Make a Deal show? Switch!

Questions? Thank you