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Dana and Alice get haircuts from the same stylist. Dana calls before lunch to book one of the open appointment times. After lunch, Alice calls and chooses from among the remaining appointments. Are these two events dependent or independent?

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Full solution

Q. Dana and Alice get haircuts from the same stylist. Dana calls before lunch to book one of the open appointment times. After lunch, Alice calls and chooses from among the remaining appointments. Are these two events dependent or independent?
  1. Dana books appointment before lunch: Dana books an appointment before lunch, choosing from all available times.
  2. Alice books appointment after lunch: Alice books an appointment after lunch, choosing from the remaining times after Dana's choice.
  3. Events dependent on Dana's choice: If Dana's choice of appointment time affects the choices available to Alice, then the events are dependent.
  4. Influence on Alice's choices: Since the set of available appointment times for Alice is influenced by Dana's earlier choice, the events are not independent.
  5. Dependent events conclusion: Therefore, Dana booking an appointment before lunch and Alice booking an appointment after lunch are dependent events.

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