A box contains 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 probability that she chooses two biographies? Write the answer as a decimal.
Answer (2)
f i rs t b oo k : 9 n o v e l s + 7 bi o g r a p hi es + 5 re f ere n ce = 21 a ll b oo k s p ro babi l i t y : P 1 ( " c h ooses bi o g r a p hi e " ) = 21 7 = 3 1 seco n d b oo k : 9 n o v e l s + 6 bi o g r a p hi es + 5 re f ere n ce = 20 a ll b oo k s p ro babi l i t y : P 2 ( " c h ooses bi o g r a p hi e " ) = 20 6 = 10 3 t h e p ro bab l i t y t ha t A l yss a c h ooses tw o bi o g r a p hi es : P ( " tw o bi o g r a p hi es " ) = P 1 ⋅ P 2 = 3 1 ⋅ 10 3 = 10 1 = 0.1 A n s . P ro babi l i t y i s 0.1
The probability that Alyssa chooses two biographies is calculated to be 0.1. This is found by multiplying the probability of selecting a biography on the first and second choice without replacement. Therefore, Alyssa has a 10% chance of selecting two biographies successively.
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