I'm solving a single-choice question in the exam. The question has $4$ options: A,B,C,D. These are my steps:
$1$. I didn't understand any choice of the four, so I randomly selected one: A.
$2$. After $1$, I figured out that D is wrong, according to the conclusion of Monty Hall problem, I change my answer, randomly chose one between B and C, suppose B. I should change, right? :) to increase probability from $1/4$ to $3/8$.
$3$. After $2$, I figured out that C is wrong, so should I change back to A? And what's the probability of each one? What if I figured out A instead of C wrong?
Thanks!
No, your deductions about other wrong answers do not change the probability that your original randomly selected answer is correct.
A crucial piece of information about the Monty Hall problem is Monty's algorithm, which is assumed to be "open a door without the prize behind it". In an alternate universe, imagine you are the contestant who has just selected Door #1. Then, by looking in a well-placed mirror, you figure out that there's no prize behind Door #3. In this situation, there is no value for you switching from Door #1 to Door #2: both are equally likely to contain the prize.
If a game show host had been obligated to tell you that D was a wrong answer, then yes, you should switch from A to B or C. But if you simply figured out that D was wrong, then there's no value in you switching.