Probability question of a scenario with two groups
I have some data based on two groups, and want to look at inter-group probabilities for initiating business relationships.
| Group | Sample Size |
| A | 615 |
| B | 153 |
| Business relationship initiation (below - starts the relationship) (left/right - receives proposition) |
A | B |
| A | 496 | 63 |
| B | 220 | 240 |
e.g. Group A initiated 496 relationships with other members of group A and 63 relationships with members of group B; Group B initiated 220 relationships with Group A and 240 relationships with other members of Group B
How can I calculate the probability that a member of Group A meeting a member of Group B will have a business relationship proposed to them by that member of Group B?
And vice versa, a member of Group B meeting a member of Group A will have a business relationship proposed to them by that member of Group A?
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"the probability that a member of Group A meeting a member of Group B will have..." is unclear. Do you mean: "for a randomly chosen member x of group A and a randomly chosen member y of group B, what is ...." ?
I think the answer is yes, meaning if I am a member of group A, and I meet a randomly chosen member of group B, what is the probability that they will initiate a relationship with me? And vice versa, if I'm a member of group B, and I meet a member of group A, what is the probability that they will initiate a relationship with me?
I think we lack information, even the precise definition of "relationship". Is it true that (x,y) in A x B can have at most 1 relationship, either initiated by x, or initiated by y?
Hi M F H, yes it is true, that's correct - it it true that (x,y) in A x B can have at most 1 relationship, either initiated by x, or initiated by y