Hitaro9
  • Hitaro9
[Statistics] A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 4 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 4 workers has the same chance of being selected as does any other group
Mathematics
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Hitaro9
  • Hitaro9
[Statistics] A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 4 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 4 workers has the same chance of being selected as does any other group
Mathematics
jamiebookeater
  • jamiebookeater
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Hitaro9
  • Hitaro9
What is the probability that one of the shifts will be unrepresented in the sample of workers?
Hitaro9
  • Hitaro9
I got that there are (24)(23)(22)(21)/(4)(3)(2) = 10626 possibilities (18)(17)(16)(15)/(4)(3)(2) = 3060 possibilities where graveyard is unrepresented (16)(15)(14)(13)/(4)(3)(2) = 1820 possibilities where swing is unrepresented (14)(13)(12)(11)/(4)(3)(2) = 1001 possibilities where day is unrepresented So the total probability is (3060+1820+1001)/10626 = .5535, which is incorrect.

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