Chances of a certain set of letters appearing?
Chances of a certain set of letters appearing?
After a debate with my dad about 5 letter words on Countdown, what are the chances that there will be one round in which the only word that can possibly be made with the given vowels and consonants is IMAGO? Is it likely, unlikely, almost impossible? As my weak point is maths (and I say this often!), can any statistics geniuses explain this in a statistics for dummies way?
Thanks very much!
Thanks very much!
- Kirk Bevins
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Re: Chances of a certain set of letters appearing?
It's impossible for it to be the only word in a selection as AMIGO will always come with it!
- Michael Wallace
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Re: Chances of a certain set of letters appearing?
Do you mean the probability that, anagrams aside, IMAGO is the only 5, and there are no longer words?
(edit: Since with things like this it's fairly important to set out the problem precisely)
(edit: Since with things like this it's fairly important to set out the problem precisely)
Re: Chances of a certain set of letters appearing?
Ah, thanks! I mean precisely what you said, Michael- anagrams aside.
- Charlie Reams
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Re: Chances of a certain set of letters appearing?
Thank you very much for your help! Compared to other letters rounds, I'm assuming that the chances of this NOT happening are rather high?
- Charlie Reams
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Re: Chances of a certain set of letters appearing?
Well, the chance of it not happening appears to be 107815 out of 107816, which is pretty high.Hannah O wrote:Thank you very much for your help! Compared to other letters rounds, I'm assuming that the chances of this NOT happening are rather high?
Re: Chances of a certain set of letters appearing?
Thanks muchly, you have helped me win the debate! Should I lock this topic now the problem is solved?
- Charlie Reams
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Re: Chances of a certain set of letters appearing?
We don't usually lock things around here (unless Brian Whitworth starts any more topics.) You might get a more theoretical answer from the Raccoon if you leave it open.
- Michael Wallace
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Re: Chances of a certain set of letters appearing?
Liek totally.Charlie Reams wrote:You might get a more theoretical answer from the Raccoon if you leave it open.
...
Actually I can't be bothered, because I just started explaining, and it takes long enough to calculate the probability of getting the letters IMAGO in the first place, and that's before you get to the 'difficult' bit. It's theoretically easy, just really really tedious to work it all out.