5 Heads and Tails

Dan, Sam, Dimitri, Angie and Joe are playing a game in which each one has a fair coin and everyone tosses it at the same time. If, in the result, there are more heads than tails, the owners of the tail coins lose. If there are more tails than heads, the owners of the head coins lose. If the 5 coins are all heads, or all tails, they repeat the process until someone loses (or some of them).

If the probability that Dan does not lose can be expressed as \(\dfrac { a }{ b } \), where \(a\) and \(b\) are coprime positive integers, find \(a+b\)

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