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The fact that the two people are picking alternately first from one class and then from the second means that the first picker always has first selection from whoever is remaining in each class; thus for the first picker:

pr(1st girl) = 12/(12+13) = 12/25

Pr(2nd girl) = 11/(11+10) = 11/21

→ Pr(two girls picked) = pr(1st girl) × pr(2nd girl) = 12/25×11/21 = 44/175

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Q: What is the probability when two people alternately are picking first from a class with 12 girls and 13 boys and then from a class with 10 boys and 11 girls that the first will pick two girls first?
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