1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability help please

  1. Oct 20, 2007 #1
    1. The problem statement, all variables and given/known data

    Suppose you throw a six-sided die five times. Find the probability that the sum of the outcomes of the throws is 15 using generating functions.

    2. Relevant equations

    Binomial theorem, generating functions

    3. The attempt at a solution

    Here's my attempt:

    Okay, so I know so far that the generating function of a single throw is
    G(x) = s/6 + (s^2)/6 + (s^3)/6 + (s^4)/6 + (s^5)/6) + (s^6)/6.

    And that G(x) raised to the 5th power is the generating function for five throws.

    Also, taking into account the independence of the x's:

    G_x(t) = ((s+...+s^6)/6)^5 = s^5 * (1-s^6)^5 divided by 6^5 * (1-s)^5.

    I get that:

    1/(1-s)^5 = 1 + (5 choose 1) s + (6 choose 2) s^2 + (7 choose 3) s^3 + (8 choose 4) s^4 + (9 choose 5) s^5

    and that

    (1-s^6)^5 = 1 - (5 choose 1) s^6 + (5 choose 2) s^12 - (5 choose 3) s^18 + (5 choose 4) s^24 - (5 choose 5) s^30

    However, I'm confused about how I use these to figure out the coefficient of s^15, which is the probability I'm looking for.
     
    Last edited: Oct 20, 2007
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Probability help please
  1. Limits Please help (Replies: 0)

Loading...