## Simulation

To determine whether one strategy (staying with your first door choice or switching to the other door) is better than the other, you will play the game 15 times with each strategy to see if you find any differences in how often you win with each strategy.

• Find a partner or a volunteer (and set up a 15 minute appointment with me) and assign one of you to be the host and one to be the contestant. Obtain 3 index cards. Mark the front of two cards as goats and the other card as a car. (Your markings should be visible to the host if held in the host's hand but not to the contestant looking at the backs of the cards only.)
• Have the host shuffle the cards and randomly arrange them with the backs of the cards facing the contestant.
• The contestant will indicate a card selection.
• The host will then reveal a goat behind one of the other two cards.

(a) Play this game a total of 15 times using the stay strategy and keeping track of whether that first door selected by the contestant reveals a car. (See the table in the Word file.)

 Game # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Outcome (car or goat)

(b) Now play the game 15 more times, this time the contestant will always switch to the other door. Keep track of whether that final door selected by the contestant reveals a car.

 Game # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Outcome (car or goat)

Because we are using the cards to represent the actual doors and you are not on national television, we are using these simulated results to represent actual plays of the game.

(c) After playing the game 30 times, what was the probability of getting a car compared to the goat using the stay strategy? Using the switch strategy?

(d) Of course, in the real game, you only get to play once. But based on the results you have so far, does it look like there is any advantage to one strategy over the other? Justify your answer.

(e) Especially if you aren't sure yet whether one strategy is better than the other, what more could you do to help you decide?