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100 people with the same driving skills went to take a driving test, 40 of them passed the test and get their driver's license. If

100 people with the same driving skills went to take a driving test, 40 of them passed the test and get their driver's license.

  1. If we record the result of the first four people who take the test, what is the probability that at least two of them passed the test?
  2. If we divide those 100 people into 10 groups of ten, what is the probability that people within the same group all have the same test results?
  3. If we stand at the front of the DMV and ask people if they passed the test, what is the probability that we asked more than 5 people to find the first new licensed driver?
  4. What are the PDF and CDF of "ask X people to have the first one who passed the exam"?
  5. If the test becomes a hundred times harder than before (only one out of a hundred can pass), what is the probability that more than 10 people passed within 1000 people?

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