A famous problem in probability comes from the game show “Let’s Make a Deal.” In it, a...

A famous problem in probability comes from the game show “Let’s Make a Deal.” In it, a contestant is shown three doors. Behind one door is a new car, and behind the other doors, there is nothing. The contestant is asked to pick one of the three doors. The host then opens up one of the two that was not chosen which always reveals that there is nothing behind that opened door. The contestant is then asked if he or she would like to change their chosen door to the other unopened one.

A) Should he/she? Explain why or why not. (Expresses opinion about whether the contestant should change his/her decision, and supports that opinion through sound application of the concepts of probability)

B) Can you think of another example where someone's intuition about probability may lead them down the wrong path?

Solutions

Expert Solution

A) This is famous Monty hall problem

He/she should change his door, because

B) other example could be

You are a legally blind person looking for a disabled parking space. They come as the Os in X,X,O,X,X,O,X,X,O,… as repeated infinitely. Every third space is a disabled space. You pull into one but can’t see the markings below your car on the road. Immediately after you, The Game Show Host, Peter, pulls in right next to you - either on the left or right. Because you know that he isn’t disabled you also know that he will never park in a disabled spot. Peter has revealed the true probabilistic landscape of the parking lot. Understanding the repetition of the disabled parking spaces you restart the engine of your car and buffer out a move of one space in the opposite direction of where Peter has parked right next to you (and this is you switching your selection). Believe it or not you have probably seen this before, in real life.

orchestra answered 10 months ago

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