Interesting Riddle

I just got this off of one of my friends, its ingenious.

You are on a game show and are asked to pick your prize from behind one of three doors. Behind one door is a complete KH set including FMs and preorders of unreleased games and the systems they go on. The others have a penny (not shiny). After you pick a door the host gives you the location of one of the pennies and gives you the chance to change doors. Does this alter your chance to get the grand prize? If so how and why?

 

The answer is 47.​

 

Pretty simple, actually.

No, it doesn't alter your chances. You may think it's a 1:3 chance for picking the right door. However, that's not what's really going on. As soon as you choose a door, the host will automatically choose a door you didn't choose. Since it was predetermined that they'd reveal where one of the two pennies were, you were forced to have a 1:2 chance of picking the right door in the first place.

So, no. It wouldn't change the odds. They already decided to show you where one of the pennies were to begin with. As a result, you really only have a 1:2 chance, NOT a 1:3 chance.

 

You are both close but actually wrong. The odds are not even.

 

I hate game shows you should get the penny because they can just switch it

 

BTW since this is a point of unclarity the host makes it so you can still pick the door you first selected and he will reveal a penny regardless of the original choice.

 

Oh, that's right. Since they're the ones calling the shots, you could be screwed either way. The question shouldn't be which door holds the prize. The question is what are you choosing?

If you don't choose the correct door, you'll see the prize in the one that you didn't choose.

However, if you DO choose the correct door, what you're really choosing is the door that your prize ISN'T behind.

Get it? You choose wrong, you'll see that you're wrong. If you choose right, they'll say that's the door you didn't want.

 

Good outside the box thinking but no. The prizes won't move and you will open the doors and therefore see what's behind them

 

Another way to see it...

You start off with a 1:3 chance.

Choice 1: Set.
Choice 2: Penny 1.
Choice 3: Penny 2.

When one of the pennies is revealed, then if you switch, the results are:

Choice 1: Chosen set changes to penny.
Choice 2: Penny 1 changes to set.
Choice 3: Penny 2 changes to set.

You get 2:3 chance. So changing, doubles the chances.

 

maybe this is right

its just a game show just because they say you can haveing does mean that they will give it to you

 

We have a winner!

All right if any of you who didn't quite follow that. Here’s how it works

If you first choose the set then the other choice will be a penny and switching makes you loose.
But if you choose one of the pennies then the host is forced to reveal the other one and by switching you gain the set.
So by switching you double your odds of gaining the prize to 2/3. Not switching keeps you at the original 1/3 however.

 

Coolness!

Ha! Knew it. Having a mathematical prodigy in the family has its perks once in awhile. :xp: