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instructables

Science City at Home

The Monty Hall Problem

Back in 1963, a new television show premiered in the United States called Let’s Make a Deal. In this show the host, Monty Hall, would choose people from the audience to play games where they could win fabulous prizes from large amounts of money, furniture, and new cars. They also had a chance to win a ZONK (a bad prize that means the person lost). Many of these games seemed to be based on random chance. You may have to choose between something in a box and something behind a curtain, which gives a 50/50 (50%) chance of getting the good prize. However, there was one game that seemed to follow these rules but instead boggled mathematicians for decades.

The game begins with Monty Hall showing 3 doors to which he knows what is behind each door. Behind 2 doors is a Goat (the ZONK) and behind one door is a brand-new car. The person picks their door (Door #1), but before it is opened Monty Hall opens another one of the doors (Door #2) to show a goat. Monty Hall then asks the person if they would like to switch their door or keep what they started with. What would you do?

Many would think that they should keep their original door as to go with their “gut instinct” as it’s a 50/50 chance now that one door is opened. One door has a car and one door has a goat, but there have always been 2 goats in play. Math shows us then that it is actually better to switch as you actually have a 2/3 chance of getting the car.

Think of it like this:

There are 100 doors with 99 having goats behind them and only 1 has a car. You have a 1/100 chance of getting the car on the first try. Monty Hall then opens every other door except for door number 100 and your door to show the goats. He either chose that door randomly since you were lucky and got the car with a 1/100 chance OR he chose it because it has the car behind it, which is at a 99/100 chance. Which odds would you choose?

Key Terms

Probability – the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.

Supplies:

– 1 piece of Paper

– Pen/Pencil/Other Writing Utensil

– Scissors

– Ruler

– Coloring Utensils