P.4 Binomial Probabilities
Suppose that past experience shows that about 24% of people who book seats in the cinema don't go to the cinema eventually. For this reason, cinemas sometimes sell more tickets than they have seats, with the expectation that they will have some no-shows. Suppose that a cinema has a small hall with 25 seats and assume that people are independent of each other in whether they show up to the cinema. Suppose that the cinema consistently sells 30 tickets for every one of these movies. On average, how many visitors will be in each movie in this hall?
How often will they have enough seats for all?
- The mean number of visitors is 7.2, everyone will have a seat at about 12.1% of the movie sessions.
- The mean number of visitors is 22.8, everyone will have a seat at about 99.9% of the movie sessions.
- The mean number of visitors is 22.8, everyone will have a seat at about 87.9% of the movie sessions.
- The mean number of visitors is 7.2, everyone will have a seat at about 99.9% of the movie sessions.
- The mean number of visitors is 22.8, everyone will have a seat at about 12.1% of the movie sessions.