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-   -   Two Questions (http://archives2.twoplustwo.com/showthread.php?t=546)

08-05-2002 10:38 AM

Two Questions
 


1. How many times must you throw two dice before you are more likely than not to roll a seven?


2. Assume the chances of getting a Royal Flush on a poker machine is one in 40,000. You walk up to that machine just as someone is being paid for a Royal on it. You start playing from that point and refuse to quit until you hit. If you were to predict the EXACT number of plays you need to make to hit it, the prediction that would have the best chance of being right is what? (I happen to know the precise answer. Can you come within a hundred?)

08-05-2002 11:01 AM

Re: Two Questions
 


a) Infinity, since you're NEVER more likely to throw a 7 than the rest of the numbers....

... or only once, if you're looking to throw a 7 before any other SPECIFIC number.


b) 30K... I can't WAIT to see the precise answer.

08-05-2002 11:21 AM

Re: Two Questions
 


1. 4


2. 27726




08-05-2002 11:53 AM

No formula ...
 


... just a wild guess.


2: 20.000


Assuming the machine has no memory.

08-05-2002 12:36 PM

Re: Two Questions
 


1) An infinite number of times. There will always be 36 combinations with only 6 of these combinations equalling 7. You will therefore always be more likely to throw a number other than 7. (five times more likely)


2) The fact that it just hit a Royal should be irrelevant. My answer is 8000 attempts.


Jimbo



08-05-2002 01:32 PM

Re: Two Questions
 


1) Undefined, you're always more likeley to roll a seven.


2) 1. Since every play is independent of each other no given play is more likeley to give you a royal. The first play is the best guess then because you're at least not guessing to high, you know for certain that at that time the event has not yet occured.


I think...


Sincerely, Andreas

08-05-2002 03:13 PM

Re: Two Questions
 


1. 3.80


2. 27726 by using


log(.500)/(log(39999)-log(40000))




08-05-2002 04:23 PM

Re: Two Questions
 


1. Four rolls. 1-(30/36)^4 = 0.5177469


2. 25,285 hands. ( 1-(1/e))*40000 = 25284.812



08-05-2002 04:32 PM

Re: Two Questions
 


Would you mind walking though the though process to getting to those equations.

08-05-2002 04:40 PM

Re: Two Questions
 


Maybe somebody has gotten it already, but i haven't read the others.


1. four times


2. 27726


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