1. Twenty percent of the library books in the fiction section are worn and need replacement. Thirty percent of the nonfiction holdings are worn. The library's holdings are 25% fiction and 75% nonfiction. a) Find the probability that randomly chosen book is fiction and in good shape. ___________ b) Find the probability that a randomly chosen book is a worn nonfiction book. ___________ c) Find the probability that a book is in good shape given it is a fiction book. ___________ d) Find the probability that a nonfiction book is worn. ___________ e) Find the probability that a randomly chosen book is worn. ___________ f) Find the probability that a book in good shape is fiction. ___________ g) Find the probability that a worn book is nonfiction. ______ 2. A manufacturer buys items from six different suppliers. The fraction of the total number of items obtained from each supplier, along with the probability that an item purchased from that supplier is defective, are shown in the following table. SUPPLIER PROBABILITY OF DEFECT 1 FRACTION OF TOTAL SUPPLIED 0.05 2 0.12 0.02 3 0.16 0.07 4 0.23 0.01 5 0.35 0.03 6 0.09 0.05 0.04 a) Find the probability that an item selected at random is defective. __________ b) Find the probability that an item is defective given it came from Supplier 1. __________ c) Find the probability that an item came from Supplier 1 and is defective. __________ d) Find the probability that an item came from Supplier 1 given it is defective. __________ e) Find the probability that an item from Supplier 6 is defective. __________ f) Find the probability that a defective item came from Supplier 6. __________ 1. Twenty percent of the library books in the fiction section are worn and need replacement. Thirty percent of the nonfiction holdings are worn. The library's holdings are 25% fiction and 75% nonfiction. a) Find the probability that randomly chosen book is fiction and in good shape. 0.8000 b) Find the probability that a randomly chosen book is a worn nonfiction book. 0.225 c) Find the probability that a book is in good shape given it is a fiction book. 0.8000 d) Find the probability that a nonfiction book is worn. 0.2250 e) Find the probability that a randomly chosen book is worn. 0.275 f) Find the probability that a book in good shape is fiction. 0.2759 g) Find the probability that a worn book is nonfiction. 0.8182 2. A manufacturer buys items from six different suppliers. The fraction of the total number of items obtained from each supplier, along with the probability that an item purchased from that supplier is defective, are shown in the following table. SUPPLIER PROBABILITY OF DEFECT 1 FRACTION OF TOTAL SUPPLIED 0.05 2 0.12 0.02 3 0.16 0.07 4 0.23 0.01 5 0.35 0.03 6 0.09 0.05 0.04 a) Find the probability that an item selected at random is defective. 0.0329 b) Find the probability that an item is defective given it came from Supplier 1. 0.0400 c) Find the probability that an item came from Supplier 1 and is defective. 0.002 d) Find the probability that an item came from Supplier 1 given it is defective. 0.0608 e) Find the probability that an item from Supplier 6 is defective. 0.0045 f) Find the probability that a defective item came from Supplier 6. 0.1368