Half of a floor

A number \(x \in \mathbb R\) is chosen from the closed interval \([2,10]\), the probability that \(\left\lfloor \frac x2 \right\rfloor\) is even can be expressed as \(\frac ab\), where \(a\) and \(b\) are positive co-prime integers, find \(a+b\)

Details and Assumptions

\(\left\lfloor x\right\rfloor\) is the floor function. \(\left\lfloor x\right\rfloor\) Is the largest integer not greater than \(x\). For example: \(\left\lfloor 3\right\rfloor = 3\), \(\left\lfloor 5.8\right\rfloor = 5\), \(\left\lfloor \pi \right\rfloor = 3\)

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