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Answered 2011-08-27 23:19:35

The probability that you will toss five heads in six coin tosses given that at least one is a head is the same as the probability of tossing four heads in five coin tosses1.

There are 32 permutations of five coins. Five of them have four heads2. This is a probability of 5 in 32, or 0.15625.

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1Simplify the problem. It asked about five heads but said that at least one was a head. That is redundant, and can be ignored.

2This problem was solved by simple inspection. If there are four heads in five coins, this means that there is one tail in five coins. That fact simplifies the calculation to five permutations exactly.

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