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Simple Probability Question

  1. Jan 12, 2005 #1
    An unbiased coin is tossed n times and X is the number of heads obtained. Write down an expression for the probability that X=r.

    It looks so simple yet I cant figure it out.
    Does it follow a binomial distribution ?

    Then if
    [tex]
    X[/tex]~[tex]N (n,p)[/tex]

    It follows
    [tex]
    P(X=r) = \left(
    \begin{array}{cc}
    n\\
    r
    \end{array}
    \right)
    \cdot p^r \cdot q^{n-1} [/tex]
    where [tex]q=1-p[/tex]

    But [tex] p=q=1/2
    [/tex]
    So the answer is
    [tex]
    P(X=r) = \left(
    \begin{array}{cc}
    n\\
    r
    \end{array}
    \right)
    \frac{1}{2}^{r+n-1}[/tex]

    Am I right ?

    P.S. First time using latex. It sure took long. :tongue2:
     
  2. jcsd
  3. Jan 12, 2005 #2
    when u raise the fraction by a certain power, u have to distribute the power to both the numerator and denominator
     
  4. Jan 12, 2005 #3

    Galileo

    User Avatar
    Science Advisor
    Homework Helper

    Almost. q should be raised to the (n-r)th power.

    You'll get used to it. And it looks so pretty. :biggrin:

    By the way, you don't need to use array's for displaying [itex]n \choose r[/itex]. LateX has a special command for it. Just type {n \choose r}. You can even omit the brackets.
     
  5. Jan 13, 2005 #4
    Ahh right, thx for the correction. Silly me.

    Gallieo: Thx for the tip. :)
    I gotta read through the list of latex commands but i am so busy right now, i dont have time for it.
     
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