Pilf

Six fair coins are flipped and land on a table. The expected value of the minimum number of coins that must be turned over to ensure that all the coins are the facing the same way can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

Details and assumptions

The coins are facing the same way if they all display heads, or if they all display tails.

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