8 red balls

Discrete Mathematics Level 5

You have a bag with 8 red balls in it.

Every turn you randomly select a ball from the bag. If it is red you replace it with a blue ball, and if it is blue you replace it with a red ball.

What is the expected number of turns you need to make before all 8 balls in the bag are blue?

If the answer is \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?


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