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?

  • 3
    $\begingroup$ Is the coin fair? What are your thoughts on this? What have you tried and where are you stuck? $\endgroup$
    – cardinal
    Sep 22, 2011 at 19:16
  • 1
    $\begingroup$ 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. $\endgroup$ Sep 22, 2011 at 21:18
  • $\begingroup$ 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. $\endgroup$
    – zbicyclist
    Sep 24, 2011 at 5:13

1 Answer 1


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, ...

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

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