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a box contain 9 novels, 7 biographies, and 5 reference books. Alyssa randomly chooses a book, then she randomly chooses another book without replacing the first book.

What is the probablity that she chooses two biographies? Write answer as decimal 

Verified Answer :

kate200468

\(first\ book:\\9\ novels+7\ biographies+5\ reference=21\ all\ books\\probability:\\P_1("chooses\ biographie")= \frac{7}{21} = \frac{1}{3} \\\\second\ book:\\9\ novels+6\ biographies+5\ reference=20\ all\ books\\probability:\\P_2("chooses\ biographie")= \frac{6}{20} = \frac{3}{10}\\\\the\ probablity\ that\ Alyssa\ chooses\ two\ biographies:\\P("two\ biographies")=P_1\cdot P_2= \frac{1}{3}\cdot \frac{3}{10} = \frac{1}{10} =0.1\\\\Ans.\ Probability\ is\ 0.1\)