## Stick or Switch?

During a certain game show, contestants are shown three closed doors. One of the doors has a big prize behind it, and the other two have junk behind them. The contestants are asked to pick a door, which remains closed to them. Then the game show host, Monty, opens one of the other two doors and reveals the contents to the contestant. Monty always chooses a door with a gag gift behind it. The contestants are then given the option to stick with their original choice or to switch to the other unopened door.

**Materials**** Needed for Experiment**

A Spinner with three equal areas; Adjustable Spinner, or

It is recommended that you use the following simulation. This simulation will tally the results for the ‘Switch’ and ‘Stay’ scenarios.

**The Stick Strategy Explained**

- Suppose that the spinner lands on door B. What does Monty do? (Shows you door C) What do you do? (Stick) Do you win or lose?
- Suppose that the spinner lands on door C. What does Monty do? (Shows you door B) What do you do? (Stick) Do you win or lose?
- Suppose that the spinner lands on door A. In this instance Monty shows you either door B or door C. What do you do? (Stick) Do you win or lose?

**The Switch Strategy Expalined**

- Suppose that the spinner lands on door B. Monty opens door C. You switch to the unopened door. Do you win or lose?
- Suppose that the spinner lands on door C. Monty opens door B. You switch. Do you win or lose?
- Suppose that the spinner lands on door A. Monty shows you door B or C. You switch. Do you win or lose?

** ****Your Task**

Discuss the following strategies.

**Question 1. **

Write a few sentences explaining whether you would “stay” with your original door choice or “switch” to a new door after seeing one of the choices. Explain why you would “stay” or “switch”.

**Question 2. **

Keep a tallied list of your experiment for “staying”. Copy the class list of experimental outcomes for “staying”. Write the experimental probability of “staying”. Explain how we determined this probability.

**You are to post your Results on the follwing link before the weekend to ensure everyone has adequate time to finish.**

**Also, please post up the ‘SWITCH’ results as well.**

**e.g.** After 100,000 Times

Strategy |
Won |
Lost |

Stick | 32,595 | 67,405 |

**Question 3. **

Write the experimental probability of “switching”. Explain how we determined the experimental probability.

**e.g.** After 100,000 Times

Strategy |
Won |
Lost |

Switch | 67,403 | 32,597 |

**Question 4. **

Write a few sentences comparing your original prediction in #1 to how you feel now. Would you “stay” or “switch”? Explain why. Use the experimental and theoretical probabilities we obtained during this lesson in your response.

**Explore posts in the same categories:**Mathematics

August 26, 2011 at 7:25 PM

when you stick to your initial choice, and dont change your choice, even after the host has opened the other door, you have chance a chance of (1/3) of winning the prize (in this case the “angry bird”.

when you decide to move, you have the chance of (2/3) of winning

the door you are choosing is random, but the door the host is opening is not random.

look at this senario, there a three doors, you choose one to open

(but have not opened it yet)… the chance of winning th prize is (1/3) for all the doors at the start.

but, as soon as i open any other door, which does not contain the prize, and which you have not choosen, and which has nothing hidden behind it… as soon i open it the chances for that door only IS “ZERO” for containing th prize?

right?

well now explain this… now since the other doors have the chance of (1/3), and there are only two remaining doors, closed..

then (1/3) + (1/3) = (2/3) ….

which makes it (2/3) of chances of winning the prize..

heres a good video, which explains it better… with a deck of cards aswell, just ingore the starting bit, it was lame lol

http://www.philipbrocoum.com/?p=967

August 30, 2011 at 6:55 PM

Monty’s Dilemma Assignment

Stick(won=21 out of 50 and lost=29 out of 50)

Switch(won=31 out of 50 and lost= 19 out of 50)

August 30, 2011 at 11:07 PM

Q1.

I would switch, as you will have a 2/3 chance of winning when you switch.

But if you stay, you only have a 1/3 chance of winning.

Q2.

Strategy Won Lost

Stick 20 30

Experimental Probability To Win: 40.00%

Q3.

Strategy Won Lost

Switch 28 22

Experimental Probability To Win: 56.00%

Q4.

My original prediction hasn’t changed. I would still use the ‘switch’ strategy as it has been backed up by evidence through the experiment that was conducted. Our experiment proved that the probability of winning when using the ‘switch’ is higher than the ‘stick’ strategy.

August 31, 2011 at 4:39 PM

Hey Sir, here are my results for “stay” and “switch”

“Stay”

WIN: 16

LOST: 34

“Switching”

WIN: 36

LOST: 14

September 1, 2011 at 12:27 AM

STAY

won: 17

lost: 33

SWITCH

won: 31

lost: 19

September 3, 2011 at 4:57 PM

Hey sir, my results are:

QS 1- If I was in a situation where I had to stick or switch, I would switch.

The reason for doing so is that once the host opens another door and I choose to switch, I will have a 2/3 chance of winning a certain prize.

The reason it is about a 2/3 chance is that since all the doors are a 1/3 chance and there are 2 doors left closed it would be 1/3+ 1/3 which = 2/3.

QS. 2- STICK OR SWITCH…

” STICK” – Won 12

– Lost -38

QS.3 “SWITCH”- Won- 36

– Lost- 14

QS.4- According to my expiriment, I would still stay with the switch strategy as I would have a greater chance of winning a certain prize rather than sticking.

September 4, 2011 at 10:35 PM

Stay

WIN: 18

LOST: 32

Switch

WIN: 34

LOST: 16

September 6, 2011 at 5:30 PM

I like my plan best… Pick the door that I least want and hope that when the second is opened, the door I want most is the one that is still closed… Then I can switch to the door that I actually wanted =D

So by my strategy, I have a higher chance of winning and I get to pick the door I originally wanted =D Win Win really =D