October 14, 2008

Time for a quiz

Here's a probability problem for you to chew on…

A contestant on a game show gets to pick 1 of 3 doors. Behind one door is a car. There is nothing behind the other two doors. The contestant chooses Door 1. The host, who knows where the car is, opens Door 3 to reveal to the contestant that there is nothing behind Door 3. He then asks the contestant if she now wants to pick Door 2 instead of Door 1.

Is it to the contestant's advantage to switch her choice?

5 comments:

Laurel said...

I know it's a trick question, but I still stand by 50/50.

Eva said...

I don't want to give it away. You have to see the movie "21" with Kevin Spacey to find out the answer. This movie is all about statistics.

Jeff Holman said...

I actually just added "21" to my Netflix queue yesterday. I read and loved "Bringing Down the House," the book on which I understand the movie was based. The problem I posted above came from a book I'm currently reading: The Drunkard's Walk: How Randomness Rules Our Lives. I'll share the answer in a few days.

Anonymous said...

you're killing me. --Andrea

Anonymous said...

OK, so Craig figures it this way: he's revealed one door, so he's now giving you this choice: do youwant door 1 or do you want 2/3. You shcould pick door 2 because he's eliminated door 3 as a choice, increasing the odds it's door 2, so it's 66% likely to be door 2 and 33% to be door 1. Still seems weird to me. -Andrea