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Math Help - Probability-Sequences of Events

  1. #1
    Yan
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    Probability-Sequences of Events

    Suppose you roll a fair six-sided die repeatedly until the first time you roll a number that you have rolled before.
    a)For each r=1,2,…calculate the probability pr that you roll exactly r times.
    b)Without calculation, write down the value of p1 + p2 + . . . +p10. Explain.
    c)Check that your calculated values of pr have this value for their sum.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Yan View Post
    Suppose you roll a fair six-sided die repeatedly until the first time you roll a number that you have rolled before.
    a)For each r=1,2,…calculate the probability pr that you roll exactly r times.
    b)Without calculation, write down the value of p1 + p2 + . . . +p10. Explain.
    c)Check that your calculated values of pr have this value for their sum.
    a) Let p(n) denote the probability of exactly n throwns before a repeat is obtained:

    p(1)=0
    p(2)=(1-p(1)(1/6)
    p(3)=(1-p(2)-p(1))(2/6)

    p(n)=(1-p(n-1)-p(n-2)-..-p(1))[(n-1)/6]

    n=1, .. ,6 and p(n)=0 for n>6

    RonL
    Last edited by CaptainBlack; October 5th 2008 at 01:56 AM.
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  3. #3
    Yan
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    how to answer the part b and c?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Yan View Post
    how to answer the part b and c?
    For part b you have to think about what the question means, then when you have part b part c follows just be using the result of a and comparing the sum with what you will know from thinking about what b is asking for.

    RonL
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  5. #5
    Yan
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    I don't get what is this question mean, can you explain to me!!
    Thanks
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by Yan View Post
    I don't get what is this question mean, can you explain to me!!
    Thanks

    If I throw 10 six sided dice what is the probability that they all show different faces.

    RonL
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