# 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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