Balcony seating at the opera is by ticket only, and all the tickets are sold and all the ticketholders are in line to enter. But it turns out that the first person through the door is rather inebriated by the time the hall is open for seating and, instead of taking the properly assigned seat, chooses a chair at random (presumably the one with the lowest-seeming relative velocity to his or her person). The next people come in one at a time—and if their seat is available, they take it. But if someone is already sitting there, rather than disrupt things, they just pick some other random seat. Which raises the question, "what is the probability that the last opera lover ends up in his or her assigned seat?"

## Question

## BMAD 65

Balcony seating at the opera is by ticket only, and all the tickets are sold and all the ticketholders are in line to enter. But it turns out that the first person through the door is rather inebriated by the time the hall is open for seating and, instead of taking the properly assigned seat, chooses a chair at random (presumably the one with the lowest-seeming relative velocity to his or her person). The next people come in one at a time—and if their seat is available, they take it. But if someone is already sitting there, rather than disrupt things, they just pick some other random seat. Which raises the question, "what is the probability that the last opera lover ends up in his or her assigned seat?"

## Link to post

## Share on other sites

## 5 answers to this question

## Recommended Posts

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.