Probability of throwing same sequence of 13 heads or tails

Question

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.

For example: Heads, Heads, Tails, Heads, Tails, Tails, Tails, Heads, Tails, Heads, Heads, Tails, Heads.

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, Commented Sep 22, 2011 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, Commented Sep 22, 2011 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, Commented Sep 24, 2011 at 5:13

johanvdw · Accepted Answer · 2011-09-23 08:39:37Z

2

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, ...

answered Sep 23, 2011 at 8:39

johanvdw

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$\begingroup$ (+1) But this was tagged as homework so you're not encouraged to just give the full answer. $\endgroup$
– Macro
Commented Sep 23, 2011 at 21:07
$\begingroup$ (sorry - didn't know that rule) $\endgroup$
– johanvdw
Commented Sep 23, 2011 at 21:42

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