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Question
I would like to find out the probability of the following result, ideally with your showing how you derived the answer, the probability or statistical rule used, and pointing out any potential error(s) in my setting up of the scenario:

Assume that each year for 25 years, 10 different, qualified people from a given group (let's say an ethnic minority) apply for a job at a company that gets 100 applicants for every position it fills. Thus, the chance of one of these 10 persons getting hired in any given year = 10 x 1/100 = 10%.

Question: what are the odds that none ever gets hired during the 25 years?

Answer
There are two principles you can use here:

First, if an event has probability p and another event has probability q, if they are not dependent on one another, the probability of both is the product pq.

Second, if an event has probability p, the probability that event doesn't happen is 1-p.



From this, you can say that every year, you have a 1 - 1/10 = 9/10 chance of not hiring one of these people. Then, over 25 years, the chances you never hire one would be:

9/10 9/10 ... 9/10 = (9/10)^25 ≈ 0.0718

Now, that is your answer. However, in asking this question you make two assumptions that are probably not true in real life. First, these events are probably not independent. Who you hire one year affects who you hire the next year. Second, there is no reason to believe that hiring people is random, meaning that the figure 1/10 is totally unreasonable. No part of hiring is random, really.

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Clyde Oliver

Expertise

I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.

Experience

I am a PhD educated mathematician working in research at a major university.

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AMS

Publications
Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

Education/Credentials
BA mathematics & physics, PhD mathematics from a top 20 US school.

Awards and Honors
Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

Past/Present Clients
In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.

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