Let \(x\) be chosen at random from the interval \((0,1)\) . What is the probability that \(\lfloor\log_{10}4x\rfloor-\lfloor\log_{10}x\rfloor=0\,? \)Here \(\left\lfloor x\right\rfloor \) denotes the greatest integer that is less than or equal to \(x\)
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+23246 In the range 0.000 < x < 0.025 the value will be -2 - (-2) = 0. ---> 0,025 - 0.000 = 0.025
In the range 0.100 < x < 0.250 the value will be -1 - (-1) = 0 ---> 0.250 - 0.100 = 0.150
The value won't be zero for all x in the range (0,1).
0.025 + 0.150 = 0.175
The full distance from 0.000 to 1.000 = 1.000
Probability = 0.175 / 1.000 = 0.175
