Despite taking several statistics courses in college years ago, I've never had a mind for probabilities, so please excuse what may be a very basic question.
To make this fun, let's say you are in a haunted house and I am giving probabilities on encountering ghosts, room by room. Here are the probabilities:
- 1/12 chance of encountering exactly 1 ghost in the dining room
- 1/16 chance of encountering exactly 2 ghosts in the kitchen
- 1/4 chance of encountering exactly 1 ghost in the bedroom
- 1/30 chance of encountering either exactly 2 ghosts or exactly 8 ghosts in the cellar
- 1/36 chance of encountering either exactly 3 ghosts or exactly 18 ghosts in the library
Probabilities are all or nothing. In the dining room, for example, there is an 11/12 probability of encountering zero ghosts.
These probabilities are independent of each other (e.g., encountering a ghost in one room does not affect whether or not you will encounter a ghost in another room).
Here are my questions (assume you enter every room):
- What is the probability you will encounter at least one ghost?
- Including upper and lower bounds, how many ghosts can you expect to encounter, if any?
Abstractions are helpful, but please also solve the problem with the concrete values above so I have an easier time mapping your work to an abstracted solution. Thank you!