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The probability of 10 heads if you toss a fair coin 10 times is

$$ P(10H) = (1/2)^{10} = 0.1 \%$$

What is the probability of some coin getting 10 heads if you toss 1000 fair coins 10 times each ?

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$ P(\text{a coin get 10 heads}) = 0.5^{10} $

$ P(\text{a coin doesn't get 10 heads}) = 1 - 0.5^{10} $

$ P(\text{all coins don't get 10 heads}) = (1 - 0.5^{10})^{1000} $

$ P(\text{at least one coin gets 10 heads}) = 1 - (1 - 0.5^{10})^{1000} \approx 0.624 $

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    $\begingroup$ for formatting formulas you can use $\TeX$ (I edited your answer). By the way, could you please describe why you consider this approach correct? $\endgroup$ – Tim Nov 23 '15 at 9:34
  • $\begingroup$ P(no coins get all heads) + P(some coins get all heads) = 1. And you can reformulate that as P(no coin get all heads) + P(at least 1 coin get all heads) = 1 $\endgroup$ – Yurii Nov 23 '15 at 9:43
  • $\begingroup$ That is why you should add more details to your answer because it is not clear. $\endgroup$ – Tim Nov 23 '15 at 9:45
  • $\begingroup$ Well, often it is enough just to give a hint and then everything become clear. Or is it against site policy to give hints? $\endgroup$ – Yurii Nov 23 '15 at 9:56
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    $\begingroup$ It is not against, in fact it is totally how self-study questions should be answered (see stats.stackexchange.com/tags/self-study/info). However, for your answer to be usable for other users and other questions you should provide a description that enables reader to extrapolate your answer to other problems. $\endgroup$ – Tim Nov 23 '15 at 9:59

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