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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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 Mar 24, 2020
 #1
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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

 Mar 24, 2020
 #2
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it's wrong!! :(((( 

Guest Mar 25, 2020

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