Hardest Riddle ever!!!?

Question

your in a game show. there are three dorrs. door a), b) and c)
one has a million dollars the other two have nothing. u pick a door, one other containing nothing is revaeled. no therre is just the door u picked and the other. you are offered to keep ur door or take the other unopened door. if you keep ur door what are the chances of getting the million dollars and if u switch what are the chances.

i know the answer and its not 50/50
if you want to see if you got i rite email me @ [e-mail]

Answer 1

The answer is 2/3 if you switch. This is because you know the host *must* open an empty door.

The easiest way to think about it is in this way. You have a 1/3 chance of picking correctly on the first pick and a 2/3 chance of being wrong. What essentially is happening is that the host is telling you "You can bet that you were correct with the first pick(1/3), or you can bet that you were wrong (2/3). *If* you were wrong with your first pick I will show which of the other two doors it was."


Another way to think about it is imagine there were 10 doors. You get one pick (1/10). Then the host shows you 8 empty doors and says would you like to keep yours or switch to the remaining door. The chances that you were correct on your first pick is still 1/10. You already knew that there were at least 8 empty doors left. He is saying, "if you were wrong with your first pick (9/10), I'll show you which one was correct."

Answer 2

It is 50/50... I can't be any different. It was initially 1 in 3 once you take away one door there are only 2 doors which makes the odds 1 in 2.

Answer 3

you switch doors because you have a 2/3 chance of winning.