An analytical solution to Monty Hall

Here how the problem goes:

First, we define three random variables:

The question says that we selected the door 1 and the host opened the door 3. We have two options: sticking to the door 1 or switching the door 2. We need to compute two probabilities:

If option 2 is greater than 1, then we should switch to door 2. Otherwise, we should stick to the door 1.

We need to compute two probabilities. It does not matter which one to compute because they sum to 1 as explained above. So, lets start computing option 2.

Applying the Bayes rule twice:

Lets look at the terms one by one:

Putting everything together:

Now, lets make the question a little more complicating and have 10 doors. We select door 1, then the host opens 8 doors (doors 2,3,4,5,6,7,8,9) leaving one door closed (door 10). Then, he asks if want to switch or not. I will show that the framework presented above can also be followed to solve this problem. We have two probability to compute:

Related posts:

Old stories create fears in children

Retribution bias is triggered in the presence of wrongdoing, or the perception of wrongdoing. It depends, in the American context, on the criminal justice system to name who is trustworthy, hirable…

So this week I stumbled upon this question on the timeline of my Facebookfriend Patty Golsteijn and boy am I ready to give you an answer on that one. Because can I be completely honest with you? I…