Results 1 to 8 of 8

Math Help - Transcendental Dice Rolls

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    Kota
    Posts
    73

    Transcendental Dice Rolls

    Three fair 6-sided dice each have their sides labeled0,1,e,π,i, (2)^(1/2). If these dice are rolled, the probability that the product of all the numbers on the top face is real can be expressed as ab, where aand b are coprime positive integers. What is the value of a+b?
    I am not able to think much more over it as what to these SPECIAL numbers....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,669
    Thanks
    1618
    Awards
    1

    Re: Transcendental Dice Rolls

    Quote Originally Posted by geniusgarvil View Post
    Three fair 6-sided dice each have their sides labeled 0,1,e,π,i, (2)^(1/2). If these dice are rolled, the probability that the product of all the numbers on the top face is real can be expressed as ab, where aand b are coprime positive integers. What is the value of a+b?

    The difficulty here is the word co-prime.
    Not everyone accepts this convention, "The numbers 1 and −1 are coprime to every integer, and they are the only integers to be coprime with 0." See this page.

    Thus any triple that contains at least one zero has the given property.
    There are 6^3-5^3 of those.

    But so does the triple (1,1,1), as does (1,\sqrt2,\sqrt2) (there are three of those).

    The triple (1,i,i) also (three of them).

    Now I have no idea why it would ask "What is the value of a+b?"

    For many reasons, I think this is a flawed question.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778

    Re: Transcendental Dice Rolls

    Quote Originally Posted by Plato View Post
    The difficulty here is the word co-prime.
    I am not sure what the difficulty is. The property in question is not that the numbers on the top face are coprime, but that the product of those numbers is real. This happens iff i appears exactly 0 or 2 times.

    My guess the reason the question asks for a + b where a / b is the required probability is that there is an automated system that accepts one integer number only, so it is not possible to enter a/ b directly. Of course, a / b is the actual answer.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,669
    Thanks
    1618
    Awards
    1

    Re: Transcendental Dice Rolls

    Quote Originally Posted by emakarov View Post
    I am not sure what the difficulty is. The property in question is not that the numbers on the top face are coprime, but that the product of those numbers is real. This happens iff i appears exactly 0 or 2 times.
    I understand about the product. The product must equal the product of integers that are co-prime.
    The difficulty is that I have seen an author who does not think that zero is co-prime with any integer. I can also think that may be true of one.

    But I do accept the Wikipedia convention.

    Also e\text{ or }\pi cannot appear at all.

    We could have (1,\sqrt2,\sqrt2), but not (\sqrt2,\sqrt2,\sqrt2).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778

    Re: Transcendental Dice Rolls

    Quote Originally Posted by geniusgarvil View Post
    If these dice are rolled, the probability that the product of all the numbers on the top face is real can be expressed as ab, where a and b are coprime positive integers.
    Quote Originally Posted by Plato View Post
    I understand about the product. The product must equal the product of integers that are co-prime.
    No, the question doesn't ask to find the probability that the product of the top numbers is a product of coprime integers. Rather, it asks to find the probability that the product of the top numbers is real, and that probability is expressed as a / b where a and b are coprime.

    Only after writing this I noted that the OP wrote ab instead of a / b; hence the confusion. I still think that my interpretation is right. Similar questions about finding a fraction and requesting the sum of the numerator and the denominator have been posted before. I know what you are thinking. Just please don't kill the OP.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,669
    Thanks
    1618
    Awards
    1

    Re: Transcendental Dice Rolls

    Quote Originally Posted by emakarov View Post
    No, the question doesn't ask to find the probability that the product of the top numbers is a product of coprime integers. Rather, it asks to find the probability that the product of the top numbers is real, and that probability is expressed as a / b where a and b are coprime.

    Only after writing this I noted that the OP wrote ab instead of a / b; hence the confusion. I still think that my interpretation is right. Similar questions about finding a fraction and requesting the sum of the numerator and the denominator have been posted before. I know what you are thinking. Just please don't kill the OP.
    I am really against guessing at what the OP really meant. That is not what is posted, is it?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778

    Re: Transcendental Dice Rolls

    I agree about not guessing. Usually by responding to the straightforward but probably wrong interpretation of the question (e.g., when necessary parentheses were omitted), I hope to shame the OP and make him/her work harder. I just want to point out that the phrase "the probability that the product of all the numbers on the top face is real can be expressed as ab" does not mean that the product can be expressed as ab: in this case it has to say say, "the probability that the product... is real and can be expressed...". So it is the probability that can be expressed, not the product of the top numbers.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,669
    Thanks
    1618
    Awards
    1

    Re: Transcendental Dice Rolls

    Quote Originally Posted by emakarov View Post
    I agree about not guessing. Usually by responding to the straightforward but probably wrong interpretation of the question (e.g., when necessary parentheses were omitted), I hope to shame the OP and make him/her work harder. I just want to point out that the phrase "the probability that the product of all the numbers on the top face is real can be expressed as ab" does not mean that the product can be expressed as ab: in this case it has to say say, "the probability that the product... is real and can be expressed...". So it is the probability that can be expressed, not the product of the top numbers.
    I just disagree.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 19th 2010, 04:49 AM
  2. Varying Dice Rolls in Order
    Posted in the Statistics Forum
    Replies: 6
    Last Post: June 4th 2010, 04:36 PM
  3. Replies: 7
    Last Post: April 14th 2010, 07:09 AM
  4. Pair of dice question, P(at least 4 rolls)
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: October 4th 2009, 11:53 PM
  5. Math Dice rolls
    Posted in the Statistics Forum
    Replies: 3
    Last Post: November 30th 2006, 02:35 PM

Search Tags


/mathhelpforum @mathhelpforum