Simple Probability Question

  • Thread starter Ryoukomaru
  • Start date
  • #1
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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:
 

Answers and Replies

  • #2
1
0
when u raise the fraction by a certain power, u have to distribute the power to both the numerator and denominator
 
  • #3
Galileo
Science Advisor
Homework Helper
1,989
6
Ryoukomaru said:
[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]
Almost. q should be raised to the (n-r)th power.

P.S. First time using latex. It sure took long. :tongue2:
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.
 
  • #4
55
0
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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