Every once in awhile, I have to go on a streak of public education for the betterment of society. The Monty Hall problem presents such an opportunity and just cause for such evangelism, as this non-intuitive probability problem routinely trips up even sharp-minded folk. So, I present to you a problem:
Suppose you're on a game show. You've made it to the final round, and there are three doors presented. Two of the doors have a goat behind them, meaning you win nothing, and the third holds a new car. Choose the door with the car, and you win that. You make your choice, and before revealing your choice, your host (Monty Hall, hence the name) opens one of the remaining two doors to reveal a goat. He then asks you if you'd like to switch. Is it advantageous to switch doors? What is your probability of winning if you do/do not switch?
...think about it...
...got an answer in mind yet?
The surprising answer is that switching gives you a 2/3 chance of winning. Most people guess 1/2 - there are two doors remaining, and one of them is right. However, let's think of this differently.
When you first choose, you have a 1/3 chance of getting the right door. Then, an incorrect door is revealed. If you were originally right and you switch, you're now wrong. But if you were originally wrong and you now switch, you're right. Because you had an initial chance of 2/3 of being wrong, by switching you now have a 2/3 chance of being right, hence the answer.
Don't believe me? Play a few rounds online and convince yourself.
Subscribe to:
Post Comments (Atom)
0 comments:
Post a Comment