I am doubting myself, so somebody smarter than me tell me where this line of mathematical logic falters:
1.) Your initial probability of choosing the $1,000,000 case is (1/26)
2.) The probability of it being in either case at the end is 1, or 100%, however you prefer. It has to be in one of the two cases.
3.) If the probability of it being in your case is (1/26), and the probability it is in both cases combined is 1… then why is the probability of the other case not (25/26)?
But then I am confusing myself because then it seems that you could do the same thing for the $1 case. That is why I am thinking it may not matter whether you switch or stay.[/quote]
Your initial probability is 1/26, but after you eliminate one case, it is then 1/25 that it has the million. And so on and so forth, until it is 1/2. People are confusing this problem with the Monty Hall problem, but it’s different because in that scenario, the host knows which case has the $1 million dollars, whereas in this one, he has no idea. You could have picked it at any time throughout playing the game and eliminating cases, you just happened not to.