Sample size and probability hypothetical example

#1
Hi,
I am trying to figure out a sample size for the following hypothetical example:
  • Say there are 40 movie theaters in New York, 40 movie theaters in Los Angeles and 20 movie theaters in Miami. Each theater has 20 screens (rooms).
    • So 100 theaters/2,000 screens total.
  • Each theater will show a different set of films at a different number of screens. So for example:
    • Theater A shows ALADDIN on 6 screens, GODZILLA on 10 screens and MA on 4 screens.
    • Theater B shows ALADDIN on 8 screens, GODZILLA on 5 screens and MA on 7 screens.
  • I want to determine if a specific trailer will be shown on GODZILLA.
    • Some GODZILLA screens will show the trailer, other screens will not show the trailer
    • I do not know which nor how many screens will show the trailer
    • I can go verify some screens but not every single screen
  1. How many GODZILLA screens do I need to verify in order to get an appropriate sample size which will help me determine the final question of how many total GODZILLA screens are showing the trailer.
  2. What are the odds that if I go to 2 GODZILLA screens at each theater I will see the trailer I'm looking for. (Reminder: I do not know how many screens are showing the trailer in any specific location, it could be 0,1,7,13, etc.)
    • In other words there are 3 possible outcomes.
      1. The trailer was played
      2. The trailer was not played
      3. I do not know because I didn't go to that screen

Thanks!