S01E07: Couples Seating in Theater

Question:

Given that there is a movie theater and a movie is released, tickets are only given to couples, i.e. no single tickets are sold. If the couples arrive randomly and occupy two consecutive seats, once seated they don’t move and the theater stops admitting when only single isolated seats remain, then find the expected proportion of empty seats.

Additional Questions:

Can you imagine this scenario for 3 or 4 seats?

What if there are infinite seats? what do you think would be the proportion of empty seats, if couples have tendancy to have an empty seat between them and the other couples besides them?

What are the worst case and best case scenarios for this problem?

How is this problem different from the previous problem of house bombing?

What if we change this from couples to triplets, how will it effect things?

Coding Assignments:

Create simulations of these questions and observe the outputs carefully.

Create visualizations / notes to see this problem visually and understand the intuition.

Use statistical knowledge to find the measures and distribution of the number of empty seats, analyze it and figure out why is it like this?

Derive formulas for all these questions emperically or theoretically and verify them mathematically if possible.

Research about this problem and its applications.

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