Probability & Statistics/probability calc

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Question
Dear Mr. Oliver,
I have the following question.
I have 40 people and I run 20 lotos monthly to select one of these peoples (20 consecutive days). Every time that one people is selected is left out of the game. It means that the first loto run will be 40 participating, the second loto run only 39 and so on, so at loto 20 will be 21 people participating. The question is which is the probability for each person to be selected in one of these 20 lotos in one month. Thanks in advance for the answer.
Regards,
George

Answer
You are choosing 20 of 40 -- that's half of the people. For person X among the group, half of the combinations include X and half do not. The probability of choosing person X is 1/2.

If order is irrelevant, as you seem to say, then the probability of one individual among the 40 people being chosen overall is 1/2. (Yes, it is that simple.)

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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.

Organizations
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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