Question

I have three slips of paper. On one of them I have written the letter A and on the other two I have written the letter F. The papers are face down so only I know what is written on each slip. I ask you to choose one of these slips, as this will determine your letter grade for the course. Yikes! You make your choice, but before I reveal your fate, I turn over one of the other slips and reveal an F (whew!), and then offer you the choice to either keep your slip or exchange it for the other yet-to-be-revealed slip. The question is... do you "keep" or "exchange"?

A) Keep
B) Exchange
C) No Difference
D) Depends on personal preference

Answer 1

It is advantageous to exchange the slip of paper, as doing so increases the probability of obtaining a slip with the letter A from 1/3 to 2/3, based on the Monty Hall problem principles.

Step-by-step explanation:

The problem is a classic example of probability and is known as the Monty Hall problem. Initially, there is a 1/3 chance that you picked the slip with the letter A, and a 2/3 chance that you picked a slip with the letter F. When one of the remaining slips is revealed to be an F, if you had initially picked an F (which had a 2/3 chance), the last slip must be A. However, if you initially picked A (with a 1/3 chance), the last slip is definitely an F. So, if you stick with your initial choice, you still have a 1/3 chance of having selected the A. But if you exchange the slip, because there was a 2/3 chance you initially picked an F, there is now a 2/3 chance the unturned slip is the A. Therefore, you should exchange your slip.