A retail giant, Mississippi, sells books on its website. The book Lisa Panner and the Accountant’s...
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A retail giant, Mississippi, sells books on its website. Thebook Lisa Panner and the Accountant’s Ledger (LP for short) is soldin the hardcover version, paperback version, audiobook version, orthe e-book version to be read on its proprietary device Ignite. Itis known that no one buys both hardcover and paperback of LP, andno one buys both hardcover and e-book. It is also known that nocustomer buys all three of paperback, e-book and audiobook. Of thecustomers interested in LP, Mississippi has found that 15% havebought the hardcover, 35% have bought the paperback, 30% havebought the audiobook and 25% have bought the e-book. Furthermore,40% have bought either the hardcover or the audiobook, and 10% havebought both the paperback and the audiobook.
(a) What fraction of the interested customers have bought boththe hardcover and the audiobook?
(b) What fraction of the interested customers have boughtexactly one of the paperback or the audiobook?
(c) (Somewhat hard) If 5% of interested customers have boughtboth audiobook and e-book, what fraction have bought only theaudiobook? (Hint: Drawing the Venn diagram will be helpful. Try tobreak the set of customers who bought an audiobook into mutuallyexclusive sets so that you can use additivity.)
A retail giant, Mississippi, sells books on its website. Thebook Lisa Panner and the Accountant’s Ledger (LP for short) is soldin the hardcover version, paperback version, audiobook version, orthe e-book version to be read on its proprietary device Ignite. Itis known that no one buys both hardcover and paperback of LP, andno one buys both hardcover and e-book. It is also known that nocustomer buys all three of paperback, e-book and audiobook. Of thecustomers interested in LP, Mississippi has found that 15% havebought the hardcover, 35% have bought the paperback, 30% havebought the audiobook and 25% have bought the e-book. Furthermore,40% have bought either the hardcover or the audiobook, and 10% havebought both the paperback and the audiobook.
(a) What fraction of the interested customers have bought boththe hardcover and the audiobook?
(b) What fraction of the interested customers have boughtexactly one of the paperback or the audiobook?
(c) (Somewhat hard) If 5% of interested customers have boughtboth audiobook and e-book, what fraction have bought only theaudiobook? (Hint: Drawing the Venn diagram will be helpful. Try tobreak the set of customers who bought an audiobook into mutuallyexclusive sets so that you can use additivity.)
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