Honey Pot III

In Hundred Acre Wood, there are 5 holes in a row. Rabbit likes to hops between consecutive holes. At any hole \(1<i<5\), she is twice as likely to jump to the left (\(i-1\)) hole as the right (\(i+1\)) hole.

Tiger playfully steals two of Winnie's favorite honey and hide them in the first and last hole. Rabbit starts hoping at the fourth hole. The expected number of hops before she lands on any of the holes that contain honey can be expressed as \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime integers. What is the value of \(a+b\)?


You are advised to solve the previous version of this problem first.
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