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Math Help - Probability Trouble

  1. #1
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    Probability Trouble

    So here's the problem:

    A five-sided die has the numbers 1-5 on each side. What is the probability, after 6 rolls, of rolling a 1 or a 2 four times only?

    I could do the problem if:

    It only dealt with one side of the die instead of two
    It didn't specifically ask for four times, but the probability of a 1 or a 2 occurring at all.

    Thank you so much!
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  2. #2
    Member kalyanram's Avatar
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    Re: Probability Trouble

    Discard this argument I messed up the calculation of probabilities follow the argument by Plato




    Every roll has 5 possible outcomes therefore total number of outcomes = 5^6
    No. of ways of having 4 ones is = \binom{6}{4}.4^2 which is also the case with having 4 two only as these two events are mutually exclusive we have the probability = \frac{2.\binom{6}{4}.4^2}{5^6}
    Last edited by kalyanram; September 5th 2012 at 03:01 AM.
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  3. #3
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    Re: Probability Trouble

    Quote Originally Posted by Mwayne95 View Post
    So here's the problem:
    A five-sided die has the numbers 1-5 on each side. What is the probability, after 6 rolls, of rolling a 1 or a 2 four times only?
    This is a simple binomial probability question. There are six trials wanting four successes.
    \binom{6}{4}{\left( {\frac{2}{5}} \right)^4}{\left( {\frac{3}{5}} \right)^2}.
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