Me and my brother are currently trying to solve a debate.
The question is: Does the probability of a student guessing a perfect score on a multiple choice test go up if the student takes the test multiple times over a set period of time.
This started by us discussing the probability of guessing every question on the SAT, resulting in a perfect score. He theorizes that by taking the SAT the max number of times he can (48) before a set date (graduation), his chances of guessing a perfect score go up, due to the fact that he has taken it 48 times. We both recognize that each test attempt is an independent event and doesn't affect the outcome of another, so each individual test attempt still has the same probability of guessing a perfect score. However, he believes that by increasing the number of trials, the chance of getting a perfect score is greater.
I say that because each event is independent, each time is the same exact probability and does not change the more that you take it.
The way that makes the most sense for me to think of it is imagining 100 locks and 100 keys. You pick 1 key and 1 lock (1 test, and 1 correct set of answers). After each attempt the locks are randomized again, just like each subsequent test and correct set of answers would become random each time. Each time you try the locks (or the test), you would have a 1:100 chance regardless of how many times you try.
Which one of us (if either) is correct? And how do we go about solving this problem? Thanks in advance for the help!