The probability that the number 1 is the leading digit is [tex]0.301[/tex].
Given information:
Benford’s law states that the probability that a number in a set has a given leading digit [tex]d[/tex], is [tex]P(d) =\log(d+1)-\log(d)[/tex]
As mentioned in question,
Probability of a number in a set is given by [tex]P(d) =\log(d+1)-\log(d)[/tex].
The division property of logarithm should be use to make it as a single logarithm [tex]P(d)=\log(\frac{d+1}{d})\;\;\;\{\log(a)-\log(b)=\log\frac{a}{b}\}[/tex].
So, the probability that the number 1 is the leading digit is,
[tex]P(1) = \log ( ( 1+1)/ 1)\\P(1) = \log ( 2)\\P(1) = 0.301\\[/tex]
Hence, The probability that the number [tex]1[/tex] is the leading digit is [tex]0.301[/tex].
Learn more about Probability here:
https://brainly.com/question/23017717?referrer=searchResults
