More egg probabilities

Zethor

Zethor

Zethor

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13 Nov 2013
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Inspired by this thread:

http://forums.overclockers.co.uk/showthread.php?t=18665294

A similar game, 1 normal egg, 5 boiled ones but only 1 player: Holly!

Each egg is has a number from 1 to 6.
Holly is asked to pick a number and let's say she chooses egg no. 1.
Before she tests it, it is revealed to her that egg no.6 is in fact boiled.
She is now given the chance to change her initial pick (pick an egg from 2 to 5) or continue with her initial choice - egg no. 1.

Should Holly change her egg or not?
Does her choice matter?

:D
 
This sounds like one of these uber-complicated probability things whereby the actual mathematics mean that changing is correct, even though I can't understand why :)

I seem to remember seeing (on wizardofodds, I suspect) proof showing that knowing which Ace (which suit) is taken from a deck affects the probability differently to knowing simply that an unspecified ace is taken. I forget the exact circumstance, to be honest.
 
She probably should because her odds were 1/6 to start with and they were just reduced to 1/5. That said most probably is a load of nonsense so meh.. whatever.
 
this is on myth busters - opening doors and prizes.

From memory - it turns out if you switch then you're more likely (in practice) to get the prize.
 
It's pretty common sense when you actually think about it. She is less likely to have picked it by chance out of 6 possible eggs than when she has one revealed to her. I remember my Dad puzzling me with this when I was a kid, I got pretty angry and told him he was just plain wrong. Sorry Dad :p
 
OK so I will play the part of "stupid idiot who just doesn't get it."

When she originally picked egg no. 1 her chances of picking the normal egg was 1/6 and it is now 1/5. But knowing that egg no. 6 is boiled means that the chance that egg no. 1 is the normal egg is now 1/5, so what benefit would repicking bring?

EDIT: It appears Wiki is my friend. You are all right and I am wrong.
 
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Zethor said:
Should Holly change her egg or not?
Does her choice matter?

:D
Click to expand...

It entirely depends on whether the person who told her egg 6 is boiled or not knows which eggs are boiled as is telling the truth.

If the game organiser knows, and doesn't lie it becomes the Monty Hall problem and she should switch.

If the game organiser has no idea which eggs are hard boiled and just randomly says egg 6 is boiled then it doesn't matter whether she switches or not.
 
Stick with her original choice, there is more chance of getting the raw egg now that there are less eggs to choose from. I think.. :D
 
Switch.

Its the 3 door game, but expanded to 6 eggs.

Edit, actually, no wait, this is the inverse of the 3 door game as she is trying to AVOID the 'prize' rather than get it, so she should stick. You want the probability of getting the 'prize' to be as low as possible in this instance.
 
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