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A book can be classified as either non-fiction or fiction. 96% of books are clas

ID: 3209314 • Letter: A

Question

A book can be classified as either non-fiction or fiction. 96% of books are classified as fiction, (a) Two books are chosen at random. What is the probability that both books are fiction? (b) Five books are chosen at random. What is the probability that all five books are fiction? (c) What is the probability that at least one of five randomly selected books is non-fiction? Would it be unusual that at least one of five randomly selected books is non-fiction? The probability is (Round to four decimal places as needed.) The probability is (Round to four decimal places as needed.) The probability is. (Round to four decimal places as needed.) that at least one of five randomly selected books is non-fiction. It would not be unusual be unusual

Explanation / Answer

96% of books are classified as fiction.

Probability of a chosen book classified as fiction : P(F) = 96/100 = 0.96

Probability of a chosen book classified as non-fiction P(NF) = 1-0.96 =0.04

(a). Two books are chosen at random what is the probability that both books are fiction.

probability that both books are fiction = Probability of first book is fiction and Probability of second book is fiction

= P(F).P(F) = 0.96 x 0.96 = 0.9216

(b). Five books are chosen at random what is the probability that all five books are fiction.

probability that both books are fiction = Probability of first book is fiction and Probability of second book is fiction and  Probability of third book is fiction and Probability of fourth book is fiction and   Probability of fifth book is fiction

= P(F).P(F) .P(F).P(F) .P(F) = 0.96 x 0.96 x 0.96 x 0.96 x 0.96 = 0.8154

(c) what is the probability that atleast one of five randomly selected books is non-fiction .

Probability of atleast one of five randomly selected is non-fiction = 1 - Probability of all the five books are fiction( not non- fiction)

As calculated in (b), Probability of all the five books are fiction( not non- fiction) = 0.8154

Probability of atleast one of five randomly selected books is non-fiction = 1 - Probability of all the five books are fiction( not non- fiction) = 1- 0.8154 = 0.1846

Yes, it's unusual that atleast one of of five randomly selected books is non-fiction as the probability for that event is 0.1846 which low.

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