In a basket ball 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?

Mutually exclusive Events are those which cannot occur simultaneously, like getting both a head & a tail at single toss of a fair die

Independent Events are those, in which occurrence or non occurrence of an event doesn't effect the occurrence or probability dynamics of the other event. Eg : Probability of happy mood of two unrelated people.

Event A - Hooting for away team, & event B - wearing blue : are not mutually exclusive, as they can occur at the same time. Since of the fans hooting for away team, 67% are wearing blue, so there are people who are hooting for away team & also wearing blue.

Event A - Hooting for away team, & event B - wearing blue : are not independent, as event A effects the occurrence of event B, since people wearing blue are 67% among those hooting for away team itself.