# Simple Probability Question

1. Jan 12, 2005

### Ryoukomaru

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
$$X$$~$$N (n,p)$$

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

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

Am I right ?

P.S. First time using latex. It sure took long. :tongue2:

2. Jan 12, 2005

### ord34l

when u raise the fraction by a certain power, u have to distribute the power to both the numerator and denominator

3. Jan 12, 2005

### Galileo

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

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

By the way, you don't need to use array's for displaying $n \choose r$. LateX has a special command for it. Just type {n \choose r}. You can even omit the brackets.

4. Jan 13, 2005

### Ryoukomaru

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.