Probability with 3 sub-pools

[tmthms]

Hello there,

This is my first post here so I hope I'm doing this correctly.

The problem is as follows:

There's a country Q that has 11.4 million people.

There's a pool of 7.6 million people within that country that form group X.
Within group X, there's subgroup A that has 888K members.

There's a pool of 2.4 million people within that country that form group Y.
Within group Y, there's subgroup B that has 880K members

There's a pool of 8.1 million people within that country that form group Z.
Within group Z, there's subgroup C that has 767K members.

Members of group A, B and C, can belong to 0, 1 or 2 of the other groups.
For example: 50k members of group A can belong to group B and 20k members to group C.

How can we calculate an estimated size of group A + B + C?

 

[Steven G]

Please read the posting guidelines for this forum so you can receive help. Post back after reading the guidelines.

 

[Romsek]

I don't think there's enough info given to really estimate anything. If I had to guess I bet what they are after is

[MATH]|A \cup B \cup C| = |A| + |B|+|C| - |A \cap B|-|A \cap C|-|B \cap C| + |A \cap B \cap C|[/MATH]
[MATH]|A| + |B|+|C| = |A \cup B \cup C| + |A \cap B| +|A \cap C| + |B \cap C|- |A \cap B \cap C|[/MATH]
You could assume some probabilities of folks belonging to those various intersections and multiply them by your numbers

 

[Dr.Peterson]

Hello there,

This is my first post here so I hope I'm doing this correctly.

The problem is as follows:

There's a country Q that has 11.4 million people.

There's a pool of 7.6 million people within that country that form group X.
Within group X, there's subgroup A that has 888K members.

There's a pool of 2.4 million people within that country that form group Y.
Within group Y, there's subgroup B that has 880K members

There's a pool of 8.1 million people within that country that form group Z.
Within group Z, there's subgroup C that has 767K members.

Members of group A, B and C, can belong to 0, 1 or 2 of the other groups.
For example: 50k members of group A can belong to group B and 20k members to group C.

How can we calculate an estimated size of group A + B + C?

If this is not a complete, verbatim copy of the problem given to you, please give us the whole thing. It will also be helpful to know the context: What topic are you studying, and what ideas do you have about how to apply what you've been taught?

If this is a real-life problem, then we'd need a lot more information in order to make any sense of it at all.