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Math Help - Roll a Pair of six-sided dice 5 times and getting four 4's?

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    Roll a Pair of six-sided dice 5 times and getting four 4's?

    What is the probability of rolling a pair of six-sided dice five times and getting four 4's?

    @Plato this was the other questions I am really struggling with.


    This is what I came up with, but I'm not sure if it is correct.

    p(x=4) = C(5,4)
    (1/36)^4 (35/36)^5-4

    which equals 2.894180045
    10^-0.6 ....That looks wrong to me..?
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    Re: Roll a Pair of six-sided dice 5 times and getting four 4's?

    P(4) = 7/36

    5choose 4 ((7/36)^4)(29/36) = .0057

    so about one in 17543 attempts
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    Re: Roll a Pair of six-sided dice 5 times and getting four 4's?

    Quote Originally Posted by tdotodot View Post
    What is the probability of rolling a pair of six-sided dice five times and getting four 4's?

    When you say 'getting four 4's' do you mean a sum of four or do you mean four spots on one die?
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    Re: Roll a Pair of six-sided dice 5 times and getting four 4's?

    Quote Originally Posted by Plato View Post
    When you say 'getting four 4's' do you mean a sum of four or do you mean four spots on one die?
    ^That's how to question was worded. I think it means sum of four. (eg: 2 dots on one die and 2 dots on the other, or 3 dots and 1dot) So the Question is asking the probability of getting the sum of four, 4 times.
    Last edited by tdotodot; February 11th 2013 at 12:29 PM.
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    Re: Roll a Pair of six-sided dice 5 times and getting four 4's?

    Quote Originally Posted by tdotodot View Post
    ^That's how to question was worded. I think it means sum of four. (eg: 2 dots on one die and 2 dots on the other, or 3 dots and 1dot) So the Question is asking the probability of getting the sum of four, 4 times.

    That would be the way I would expect to read it.
    If you roll a pair of dice there are three ways to get a sum of four.

    So in five rolls getting a sum of four four times:
    \binom{5}{4}\left(\frac{3}{36}\right)^4\left(\frac  {33}{36}\right).
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    Re: Roll a Pair of six-sided dice 5 times and getting four 4's?

    Quote Originally Posted by Plato View Post
    That would be the way I would expect to read it.
    If you roll a pair of dice there are three ways to get a sum of four.

    So in five rolls getting a sum of four four times:
    \binom{5}{4}\left(\frac{3}{36}\right)^4\left(\frac  {33}{36}\right).
    Could I rewrite that as:

    p(x=4) = C(5,4) (3/36)^4 (33/36)
    p(x=4) = 2.21032664610^-04

    My calculator is outputting a weird number?

    OR is it NOT C(5,4) And just (5/4), which gives me 5.52581661510^-05

    ___Compared to what my original post shows, I was only wrong with the probability of getting a 4. I had 1/36 and 35/36 WhereAs you have 3/36 and 33/36.

    Once again -your a life saver man!
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    Re: Roll a Pair of six-sided dice 5 times and getting four 4's?

    Quote Originally Posted by tdotodot View Post
    Could I rewrite that as:

    p(x=4) = C(5,4) (3/36)^4 (33/36)
    p(x=4) = 2.21032664610^-04

    My calculator is outputting a weird number?

    \binom{5}{4}\left(\frac{3}{36}\right)^4\left(\frac  {33}{36}\right)=0.000221032664609
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    Re: Roll a Pair of six-sided dice 5 times and getting four 4's?

    Thanks, that actually looks right, unlike the number I keep getting on my calculator?!?!?! *Don't Get WHY* I tried using an online calculator, input everything exactly the same and got 0.000221032664609.... Guess there's something wrong with my calculator! JUST VERY GLAD I finished those two questions!

    0.000221032664609. ONLINE CALCULATOR
    2.21032664610^-04 MY CALCULATOR
    ^It seems as though it is just multiplying it a few thousand times? Why?
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