Identify independent and dependent events

Full solution

Q. Students are auditioning for roles in the school musical. Each student must come ready to perform a song of his or her choice in front of the judges.

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Are these two events dependent or independent?

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Choices:

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(A) dependent

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(B) independent

Understand Definitions: To determine whether the events are dependent or independent, we need to understand the definitions of these terms. Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. Conversely, two events are dependent if the occurrence of one event does affect the probability of the occurrence of the other event.
Individual Student Auditions: In the context of students auditioning for roles in the school musical, each student's performance is an individual event. The outcome of one student's audition (whether they perform well or not) does not influence the outcome of another student's audition. The judges evaluate each performance on its own merits.
Events are Independent: Therefore, the events are independent because one student's performance does not change the probability of how the next student will perform. Each student's chance to impress the judges with their song choice is unaffected by the performances of others.