​How to win a game show: Monty Hall problem

• Question: Lots of TV game shows are based on luck, but is there anything you can do to improve your chance of winning?

• For contestants of a famous game show in the 1970s, the answer seemed illogical at first and confused some mathematicians.

• The key to boosting the odds of winning lay in understanding probability, or the likelihood of something happening.

• You’re in luck! You’ve been selected to be a contestant on a TV game show, and there’s a grand prize.

• The rules are simple: You’ll be shown three doors, and all you need to do is pick one of them to win the prize behind it.

• Behind one of the doors is the grand prize, a brand-new sports car, but behind each of the other two is a goat.

  Goats are nice, but let’s assume you want to win the car.

• Behind one of the doors is the grand prize, a brand-new sports car, but behind each of the other two is a goat.

  Goats are nice, but let’s assume you want to win the car.

• It’s time to make your choice. Dramatic music plays, the spotlight shines on you. You cant put the decision off any longer-the host needs an answer.

  You pick the blue door.

• Before opening the blue door, the host helps you out a little by revealing one of the goats.

• Fact: The host knows which door the car is behind and will always open a door to reveal a goat.

• He opens the green door—a bleating goat steps forward.

• The host then asks you whether you want to stick or switch—in other words:

  Are you happy with your original choice of the blue door, or would you prefer to switch to the pink door? What do you do?