Draw me until you match me

Four balls numbered \(1,2,3,4\) are placed inside a hat. You draw a ball out of the hat, write down the number on the ball and place the ball back in the hat. You repeat this process until you have written down the same number twice.

The probability that the last ball you drew is the same as the first ball you drew can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b?\)

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