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On a rainy day an unnamed statistics professor decides to play with an urn containing bottle caps. Five were from Guinness, ten Bass, and ten Smithwicks. He picks a cap at random, looks at it, and then replaces it in his urn. He does this eight times because he is very bored.

  • What is the probability that he will pick a Guinness every time?
  • What is the probability that he will pick a Guinness exactly seven times?
  • What is the probability that he will pick something other than a Guinness exactly once?
  • What is the probability that he will pick a Guinness at most six times?
  • What is the probability that he will pick something other than a Guinness at least twice?
  • What is the mean number of Guinness caps he should see in eight trials?
  • What is the standard deviation for the number of Guinness caps appearing in eight trials?

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