Probability of r heads in n fair coin tosses

[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 can't figure it out.
Does it follow a binomial distribution ?

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

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

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

Am I right ?

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

 

[ord34l]

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

 

[Galileo]

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

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

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

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.

 

[Ryoukomaru]

Ahh right, thanks for the correction. Silly me.

Gallieo: Thx for the tip. :)
I got to read through the list of latex commands but i am so busy right now, i don't have time for it.