Question
In: Statistics and Probability
Amazen has a collection of books for sale. They are either paperbacks or hardcovers and either...
Amazen has a collection of books for sale. They are either paperbacks or hardcovers and either fiction or nonfiction. Forty percent of the books are fiction and 65% are paperbacks, Also, 25% of the fiction books are hardcover. Now, a book is selected at random.
a. What is the probability that it is a paperback?
Solutions
Expert Solution
a.
It is given that, probability that the book is a paperback = 0.65
b.
Given,
P(hardcover | fiction) = 0.25
Probability that it is a paperback, given that it is a fiction = P(paperback | fiction)
= 1 - P(hardcover | fiction)
= 1 - 0.25 = 0.75
c.
P(hardcover) = 1 - P(paperback) = 1 - 0.65 = 0.35
By Bayes theorem,
Probability it is a nonfiction, given that it is hardcover = P(nonfiction | hardcover)
= 1 - P(fiction | hardcover)
= 1 - P(hardcover | fiction) P(fiction) / P(hardcover)
= 1 - 0.25 * 0.4 / 0.35
= 0.7142857
d.
Probability it is a nonfiction, given that it is paperback = P(nonfiction | paperback)
= 1 - P(fiction | paperback)
= 1 - P(paperback | fiction) P(fiction) / P(paperback)
= 1 - 0.75 * 0.4 / 0.65
= 0.5384615
Probability it is either nonfiction or paperback = P(nonfiction or paperback)
= P(nonfiction) + P(paperback) - P(nonfiction and paperback)
= 1 - P(fiction) + P(paperback) - P(nonfiction | paperback) P(paperback)
= 1 - 0.4 + 0.65 - 0.5384615 * 0.65
= 0.9
orchestra answered 2 years agoRelated Solutions
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