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More ways to get Braingle...

Two Ones

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 

Puzzle ID:#44413
Fun:** (2.04)
Difficulty:*** (2.11)
Category:Probability
Submitted By:shenqiangAcn****!!

 

 

 



Which is more likely to happen?

1) Roll a fair die 4 times and get at least one 1;
2) Roll 2 fair dice 24 times and get at least one "double 1".





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Comments

Mill89Aus*
May 04, 2009

The latter equation should read:
(35/36)^6 (or 0.844) which is slightly larger than 5/6 (or 0.833).
xdbtcpAus*
May 04, 2009

So.....the answer is the first one or second one?
bradon182001*us*
May 07, 2009

Confusing.
Lil_Dork*ca*
May 15, 2009

weird...
javaguru*us*
Aug 12, 2009

The problem was easy enough, but the answer was not very clear. It's more likely to role the single one than the double one.

(35/36)^24 ≈ .5086
(5/6)^4 ≈ .4823

So the odds of rolling double ones is 1 - .5086 ≈ .4914 and the odds of rolling a single one are 1 - .4823 ≈ .5177.

dalfamnestAnz*
Aug 16, 2009

OK, I got it - but it's more of a textbook question than a teaser.
Juanito*
Jun 18, 2010

The probability to fail the first dice once is not 5/6 but 5/6+(1/6)*(5/6) for one time.
Juanito*
Jun 18, 2010

I was mentioning the two dice there....
mathemagicianus*
Jun 08, 2011

I teach university statistics and probablity.

javaguru is precisely correct.

X = successfully rolling a "1"
Y = successfully rolling a "double 1"

P(X>= 1) = 1 - P(X=0) = 1 - (5/6)^4

~ 0.5177 or 51.77%

P(Y >=1) = 1 - P(x=0) = 1 - (35/36)^24 ~ 0.4914 or 49.14%

So, rolling at least "one 1" is a more likely outcome than rolling at least "one double 1" by about 2.63%.
princess2007A*
Jul 27, 2011

ok. I gotta try this in about a year. XD I have no idea how you got your answers. I'm sure its good though. This goes into my favorites for now.



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