Half of a floor

Probability Level 3

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

Details and Assumptions

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

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