Probability: What are the odds?

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SUMMARY

The discussion centers on the client loss experienced by two business owners, Fred and Jeff, following a company split. Fred lost 235 clients while Jeff lost 285, prompting a debate on whether this outcome is due to random variability or a significant deviation from expected results. The analysis indicates that the situation can be modeled using a binomial distribution, with the total number of clients being 2,000, thus each owner initially had 1,000 clients. The conclusion drawn is that if the original number of clients was close to the total lost, the losses are unlikely to be random variability.

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  • Understanding of binomial distribution
  • Familiarity with normal distribution approximations
  • Basic knowledge of probability theory
  • Ability to analyze client data metrics
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  • Study the principles of binomial distribution in depth
  • Learn about normal distribution and its applications in statistics
  • Explore statistical methods for analyzing client retention and loss
  • Investigate case studies on business performance post-split
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Business analysts, statisticians, and entrepreneurs looking to understand client retention dynamics and the impact of business restructuring on client loss.

jellybean
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My company split in two.
Two owners, Fred and Jeff. Each got half the clients.
Since then, Fred lost 235 clients and Jeff lost 285.
My co-worker says it's just random variability.
I says no way, that's one in a million.
What are the odds? What's the equation?
p.s. true story
 
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Randomness would assume this is a binomial distribution with probability p1 Fred will lose a client, probability p2 Jeff will lose a client. For large numbers those can be approximated by normal distributions but to do that you would need to know the total number of clients each one started with and I don't see how you can decide whether it was "random variability" or not without knowing how many clients there were to start with. If the original number of clients was not much more than 235+ 285= 520, this is probably not "random variability". If the original number of clients was much more, then it probably was.
 
Oops, you're right. I thought at first it was just a coin toss x 520.
In round numbers, the total was 2,000. So each began with 1,000 clients.
 

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