# Probability/ Stats Puzzle – 1 (Solution)

If you have not tried to solve the puzzle, click here for the problem. The problem was discussed in an earlier post.

This is a famous puzzle, called the “Monty Hall Problem”. Monty Hall was a host in the early episodes of the game show Let’s Make a Deal.

The common version of the the puzzle used three doors (instead of 3 boxes) and a car and two goats (instead of gold and garbage).

The problem was originally posed by Steve Selvin and became famous when it was quoted by Marilyn vos Savant in Parade magazine in 1990.

The answer: You increase the probability of winning the gold if you change your choice of the box to open. The probability of winning the gold is only 1/3 if you continue with your original choice and 2/3 if you change your choice.

Here is a brief explanation of why:

When you initially selected a box, you had a 1/3 probability of being right. The host knowingly opened a box with garbage in it, so that eliminated one of the wrong choices.  You still have a 1/3 probability that you initially chose the right box; this means that the other unopened box has a 2/3 probability of containing the gold.

Amit Bhattacharjee, Satish K Mariyappagoudar, and Patrick OToole got it right.

Or you can watch the youtube video.