one tribe has 9 members, other has 7; randomly assigned to three tribes w/ 5 members; 1 left over

[NathLink13]

There are two tribes of people, one having 9 people and one having 7 people, and they are randomly put into three tribes of 5 with one person being left out. What are the odds that the tribe of 9 will have the majority in all three tribes?

 

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[khansaheb]

What are the odds that the tribe of 9 will have the majority in all three tribes?

Are you sure that the question is asking for "odds" and NOT "chances (or probability)"?

 

[ImMAD]

Assuming probability not odds, you could start with splitting the problem up in two cases. Label group of 9 as A, group of 7 as B.

Case 1: B has the one left out, hence A has 9, B has 6. Case 2: A has the one left out, hence A has 8, B has 7. Probability case A: 7/16, probability case 2: 9/16.

Next, imagine first group a is formed, then group b, then group c. Consider case 1: P(majority a,b,c) = P(majority a)*P(majority b|majority a)*P(majority c|majority in a,b).

Hope this helps you out a bit.