perplexus.info :: Probability : Assigning a wonky die

Assigning a wonky die (Posted on 2006-04-28)

I have an unfair die whose sides are known to have the following probabilities:{.02,.04,.08,.12,.24,.5}
Assign the numbers {1,2,3,4,5,6} to these sides so the expected roll is the same as for a fair die.

Can you solve this without brute force?

Submitted by Jer

Rating: 3.0000 (1 votes)

Solution: (Hide)

p(1) = .04
p(2) = .08
p(3) = .50
p(4) = .12
p(5) = .24
p(6) = .02
Is one solution, its reversal is another. I didn't know there were more (see Charlie's solution) because I never checked using brute force.
If 'brute force' means checking every possibiity, this can be solved without by putting the numbers in any order and then switching then by pairs to lead the expected value in the direction of 3.5

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Some solutions by hand	snark	2006-05-03 22:29:34
More brute force	Charlie	2006-04-28 15:01:51
re: The answer is ... the same (Spoiler)	Leming	2006-04-28 13:39:07
The answer is ...	Bob Smith	2006-04-28 12:19:48

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