I am learning probability on my own (I am not taking any class). I came across this question while learning the the binomial probability distribution formula.

How do I use the binomial distribution formula to solve the following question? What is the probability of getting six heads when flipping 10 coins 10 times.

Does it affect thing that 10 coins are flipped 10 times or 100 times?

I messed it up with the question: What is the probability of 6 heads if flipping 2 coins 5 times. Then n will be 10...

Thank you in advance!

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    $\begingroup$ stats.stackexchange.com/tags/self-study/info $\endgroup$
    – Taylor
    Commented Feb 1, 2017 at 16:51
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    $\begingroup$ I'm voting to close this question as off-topic because this is a very elementary question. $\endgroup$ Commented Feb 1, 2017 at 17:28
  • $\begingroup$ @MichaelChernick, Is it against site rules to ask elementary questions? Does that make something off topic? :-o $\endgroup$ Commented Feb 1, 2017 at 17:56
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    $\begingroup$ Elementary questions are likely to have been answered many times in possible duplicates. $\endgroup$ Commented Feb 1, 2017 at 18:28
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    $\begingroup$ Thank you for adding the [self-study] tag. Please read its wiki. You need to tell us what you understand thus far, what you've tried (other than that you've searched the internet for the answer) & where you're stuck. We'll provide hints to help you get unstuck. $\endgroup$ Commented Feb 1, 2017 at 18:58

1 Answer 1


If the probability of heads if $p$, the six heads happen with probability $p^6$ and the four tails with probability $(1-p)^4$. There are 10 possible places for the 6 heads, so you need to multiply by the number of ways that can happen: ${10 \choose 6} = 210$, so the answer is

$$ {10 \choose 6} p^6 (1-p)^4 $$

If the coin is fair, this equals $210 \times (0.5)^{10} \approx 0.20$

  • $\begingroup$ Please be cautious when answering self-study questions. It doesn't matter if the question really came from someone's homework or not. Our policy are to provide hints, not complete answers. You can see our policies here. $\endgroup$ Commented Feb 1, 2017 at 17:55
  • $\begingroup$ @gung, Ok I'll be cautious. Is it against site rules to ask elementary questions though? $\endgroup$ Commented Feb 1, 2017 at 18:07
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    $\begingroup$ That's more a discussion for meta.CV. FWIW, in my opinion, no, asking elementary questions is fine. $\endgroup$ Commented Feb 1, 2017 at 18:08
  • $\begingroup$ Thank you not_bonferroni for your fast reply! Your answer made me think once more. The thing that messed it up for me was the part "ten times". I guess it doesn't matter if you flipp ten coins ten times or 100 times... $\endgroup$
    – Marcela
    Commented Feb 1, 2017 at 18:25
  • $\begingroup$ @Marcela if there is serial dependence in the flips it could make a difference but nothing in what you wrote indicates that. I read your question as asking about ten coin flips each from different independent coins. If you meant 100 independent coin flips then replace 10 with 100 and 4 with 94 in my post above. If there is serial dependence you'd need to do something more complex. $\endgroup$ Commented Feb 1, 2017 at 18:40

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