# Probability of throwing same sequence of 13 heads or tails

Simple (I hope) probability question I'd love it if someone could answer for me.

You flip a coin 13 times (two outcomes: heads or tails).

Before the coin tossing, I've written down the 'winning sequence', eg. a random sequence of 13 outcomes, heads or tails for each toss.

What are the chances of someone tossing the coin and getting the same sequence (heads or tails in the exact same sequence) as me?

• Is the coin fair? What are your thoughts on this? What have you tried and where are you stuck? – cardinal Sep 22 '11 at 19:16
• As an addition to cardinal's comments. You might want to try experimenting with a smaller number than 13, try with just three or so to simplify the question until you get a feel for it. – Jonathan Lisic Sep 22 '11 at 21:18
• Lisic's comment is the key to a lot of probability problems. Simplify them until you can list all the outcomes -- that will help you see the pattern. Try it with just 3, and draw out a decision tree diagram. – zbicyclist Sep 24 '11 at 5:13

If you have a fair coin: $(1/2)^{13}$. $1/2$ that you have the first correct, multiplied by $1/2$ that you have the second correct, ...

• (+1) But this was tagged as homework so you're not encouraged to just give the full answer. – Macro Sep 23 '11 at 21:07
• (sorry - didn't know that rule) – johanvdw Sep 23 '11 at 21:42