JZMathTime
New member
- Joined
- Nov 1, 2019
- Messages
- 3
Imagine a situation where a number of subjects (X) are going to be offered a number of options (Y), and there's a constant probability (P) that any given subject will accept any given offer.
An option that is accepted will be "filled" by exactly one of the subjects that accepted it. And while a subject may have been willing to accept multiple options, a subject can only fill exactly one option.
I'm trying to derive a formula for the expected result of this scenario, but getting stuck. This would be extremely easy to calculate if we were just looking for the expected number of matches overall, but the fact that we're actually "filling" the options as we go is throwing me for a loop.
In other words --
Given:
Subjects are presented with Options, which they may accept or not.
An option that is accepted by any number of subjects greater than 0, will be filled by exactly one of those subjects.
Each subject can fill at most one option, but may accept more than one.
Let X = Number of Subjects
Let Y = Number of Options
Let P = Probability of a Subject accepting an Option
Define F(X,Y,P) such that it gives the expected number of options that will be filled by the subjects.
This seems like such a basic question that there must already be a formula someone derived that describes these situations, but I haven't been able to search it up online. Can anyone offer any help here?
An option that is accepted will be "filled" by exactly one of the subjects that accepted it. And while a subject may have been willing to accept multiple options, a subject can only fill exactly one option.
I'm trying to derive a formula for the expected result of this scenario, but getting stuck. This would be extremely easy to calculate if we were just looking for the expected number of matches overall, but the fact that we're actually "filling" the options as we go is throwing me for a loop.
In other words --
Given:
Subjects are presented with Options, which they may accept or not.
An option that is accepted by any number of subjects greater than 0, will be filled by exactly one of those subjects.
Each subject can fill at most one option, but may accept more than one.
Let X = Number of Subjects
Let Y = Number of Options
Let P = Probability of a Subject accepting an Option
Define F(X,Y,P) such that it gives the expected number of options that will be filled by the subjects.
This seems like such a basic question that there must already be a formula someone derived that describes these situations, but I haven't been able to search it up online. Can anyone offer any help here?