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The requirement that one coin is a head is superfluous and does not matter.

The simplified question is "what is the probability of obtaining exactly six heads in seven flips of a coin?"...

There are 128 permutations (27) of seven coins, or seven flips of one coin. Of these, there are seven permutations where there are exactly six heads, i.e. where there is only one tail.

The probability, then, of tossing six heads in seven coin tosses is 7 in 128, or 0.0546875.

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โˆ™ 2011-08-21 00:48:48
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Q: What is the probability of obtaining exactly six heads in seven flips of a coin given that at least one is a head?
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