Lemma
EasyConditional probability
OpenStax, Introductory Statistics 2e §3.2 Independent and Mutually Exclusive Events · Try It 8 · Probability · Conditional probability

Independent and Mutually Exclusive Events · Try It 8

In a basketball arena,

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

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OpenStax, Introductory Statistics 2e · §3.2 Independent and Mutually Exclusive Events · Try It 8

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