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Math Help - Probability of Independent event

  1. #1
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    Probability of Independent event

    In the popular dice game Yahtzee, a Yahtzee occurs when five identical numbers turn up on a set of five standard dice. What is the probability of rolling a Yahtzee on one roll of the five dice?

    This is my answer:

    (1/6) ^ 5 =1/7776

    However, my text has the answer as 1/1296


    Where did I go wrong, or is the text wrong?
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  2. #2
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    Quote Originally Posted by john-1 View Post
    In the popular dice game Yahtzee, a Yahtzee occurs when five identical numbers turn up on a set of five standard dice. What is the probability of rolling a Yahtzee on one roll of the five dice?

    This is my answer:

    (1/6) ^ 5 =1/7776

    However, my text has the answer as 1/1296


    Where did I go wrong, or is the text wrong?
    There are six possible numbers for which you can get a Yahtzee so you have to multiply by 6.
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    multiply (1/6)^5 by six?
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  4. #4
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    Quote Originally Posted by john-1 View Post
    multiply (1/6)^5 by six?
    Well yes (did you do that and see you got the correct answer?).
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    no i didn't get the right answer, that's why i asked you if that's what you meant
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    6 \times \left(\frac{1}{6}\right)^5 = \frac{1}{1296}

    I just checked on my calculator
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    ok.. thanks, but wait, just another question.. I'm not really sure I understand how there are "six possible numbers for which you can get a Yahtzee". I understand this part
    (1/6)^5 because that's like saying the identical numbers part, which means you get a yahtzee. But then when you multiply by six...how is there another six possibilities to get a yahtzee when the question says that it takes FIVE identical numbers out of six, to get a yahtzee. can you please explain.
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  8. #8
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    Quote Originally Posted by john-1 View Post
    ok.. thanks, but wait, just another question.. I'm not really sure I understand how there are "six possible numbers for which you can get a Yahtzee". I understand this part
    (1/6)^5 because that's like saying the identical numbers part, which means you get a yahtzee. But then when you multiply by six...how is there another six possibilities to get a yahtzee when the question says that it takes FIVE identical numbers out of six, to get a yahtzee. can you please explain.
    How many numbers are there on a die? Remember you can get a yahtzee with any of the numbers. Also assuming all the dice are fair each of the numbers has an equal chance of coming up
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    six.. so is it something to do with the identical numbers part?
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  10. #10
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    Quote Originally Posted by john-1 View Post
    six.. so is it something to do with the identical numbers part?
    As Mr F said in post 2 there are 6 numbers on a fair die. As the Yahtzee can be obtained using any number (1,2,3,4,5 or 6) this means you must multiply by 6 to compensate.

    If you're unsure list all the possible combinations

    edit: if I rolled 5 ones I would get a yahtzee. Would I have got a Yahtzee if I'd rolled 5 fours instead? What about 5 threes
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