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Back to 3.2 Independent and Mutually Exclusive Events

3.2 Exercise 14

Avg difficulty 2.5

In a basketball arena,

  • 70 percent of the fans are rooting for the home team,
  • 25 percent of the fans are wearing blue,
  • 20 percent of the fans are wearing blue and are rooting for the away team, and
  • Of the fans rooting for the away team, 67 percent are wearing blue.

Let A be the event that a fan is rooting for the away team.
Let B be the event that a fan is wearing blue.
Are the events of rooting for the away team and wearing blue independent? Are they mutually exclusive?

OpenStax Statistics, 3.2 Independent and Mutually Exclusive Events, exercise 14

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Adapted from Statistics © 2022 Rice University. Licensed under CC BY 4.0. Source: Statistics. Imported at revision 7dea80a.