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John has $\ 6 $ coins. He performs a test which involves tossing all coins simultaneously. He repeats this experiment until all coins shows up as heads. What is the probability that it takes him at least $\ 12 $ tosses to achieve this feat?

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    Until all coin shows up heads at least one or simultaneaously?2012-12-06
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    Hint: it requires at least 12 repetitions of the experiment if and only if each of the first eleven experiments resulted in at least one of the coins showing a tail.2012-12-06
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    Hint: Think of the geometric distribution.2012-12-06

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