A publisher knows that from all the writers the company published, 20% wrote romantic novels and 40% wrote sci-fi books. If we look at the last 5 years, 40% published 2 books, and 30% published only 1 book. From the writers that did not published in the last 5 years, 20% wrote romantic novels and 40% sci-fi books. From the writers that wrote other types of books, 50% published 2 books. Finally, the number of sci-fi writers that published 1 and the number that published 2 books was the same. 1. What is the average number of books published in the last five years? 2. What proportion of writers are sci-fi writers and published 2 books during the last five years? 3. What is the probability that if we choose a romantic novels writer, he had not published in the last five years? 4. What is the probability that a writer did not publish romantic or sci-fi and did not publish exactly 1 book in the past five years? 5. If we select a writer that had published in the last five years, what is the probability that he writes romantic novels? 6. If we select 5 writers, what is the probability that they didn't publish any books in the past 5 years? 7. What is the probability that a writer is not a romantic novel writer and published more than 1 book in the past five years? 8. Are types of books and the number of books published in the past five years statistically independent? 9. Is writing sci-fi books and not publishing in the last years statistically independent? 10. What is the probability that if we choose 4 writers, 2 of them have published 1 romantic novel in the last 5 years? 11. What proportion of writers did not write sci-fi and published one or two books?

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Step-by-step explanation:

A publisher knows that from all the writers the company published, 20% wrote romantic novels and 40% wrote sci-fi books. If we look at the last 5 years, 40% published 2 books, and 30% published only 1 book. From the writers that did not published in the last 5 years, 20% wrote romantic novels and 40% sci-fi books. From the writers that wrote other types of books, 50% published 2 books. Finally, the number of sci-fi writers that published 1 and the number that published 2 books was the same. 1. What is the average number of books published in the last five years? 2. What proportion of writers are sci-fi writers and published 2 books during the last five years? 3. What is the probability that if we choose a romantic novels writer, he had not published in the last five years? 4. What is the probability that a writer did not publish romantic or sci-fi and did not publish exactly 1 book in the past five years? 5. If we select a writer that had published in the last five years, what is the probability that he writes romantic novels? 6. If we select 5 writers, what is the probability that they didn't publish any books in the past 5 years? 7. What is the probability that a writer is not a romantic novel writer and published more than 1 book in the past five years? 8. Are types of books and the number of books published in the past five years statistically independent? 9. Is writing sci-fi books and not publishing in the last years statistically independent? 10. What is the probability that if we choose 4 writers, 2 of them have published 1 romantic novel in the last 5 years? 11. What proportion of writers did not write sci-fi and published one or two books?

See attachment for additional steps to get answers

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign