# 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?
• Answering this type of questions deserve a bounty!

• "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

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