What is the Monty Hall problem?

The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show “Let’s Make a Deal” and named after its original host, Monty Hall. The problem is as follows:

Premise: One of the three doors has a prize behind it, and the other two have a dud (goat).

1. The participant chooses one of the three doors.
2. The host opens one of the other two doors that the participant did not choose, revealing a dud.
3. The participant is asked whether they want to change their chosen door.

The problem is to consider whether the participant should change the door or not.

Solution

The solution to the Monty Hall problem is as follows:

1. If the participant does not change the initially chosen door

   • Probability of winning: 1/3
   • Probability of losing: 2/3

2. After the host opens the dud door

   • If not changed, probability of winning: 1/3 (Does not change from the winning probability in step 1.)
   • If changed, probability of winning: 2/3 (The probability of the remaining options.)

Therefore, the participant has a higher probability of winning by changing the door.

Reference

• Wikipedia Monty Hall problem