Faked numbers in tax returns, invoices, or expense account claims often display
ID: 3224350 • Letter: F
Question
Faked numbers in tax returns, invoices, or expense account claims often display patterns that aren't present in legitimate records. Some patterns, such as too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford's law. If you look at a company's financial records and choose one record at random, then Benford's law gives the following probability model for the first digit of the record. Note that the first digit cannot be zero. Please use this information to answer the following questions, and to receive as much credit as possible. 1. What is the probability that the first digit of a legitimate financial record is at least 6? Please explain how you reached your answer. 2. What is the probability that the first digit is not 1? Please explain how you reached your answer. 3. Are legitimate records more likely to start with an even digit or an odd digit? How do you know?Explanation / Answer
1. P(First digit atleast 6)
= P(First digit 6) + P(First digit 7) + P(First digit 8) + P(First digit 9)
= 0.067 + 0.058 + 0.051 + 0.046
= 0.222
2. P(First digit not 1)
= 1 - P(First digit 1)
= 1 - 0.301
= 0.699
3. P(First digit even)
= P(First digit 2) + P(First digit 4) + P(First digit 6) + P(First digit 8)
= 0.176 + 0.097 + 0.067 + 0.051
= 0.391
So,
P(First digit odd) = 1 - P(First digit even) = 1 - 0.391 = 0.609
Since probability of first digit odd is more than probability of first digit even, the legitimate records are more likely to start with an odd digit.
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