A book can be classified as either non-fiction or fiction. 89% of books are clas

Question

A book can be classified as either non-fiction or fiction. 89% of books are classified as fiction. (a) Two books are chosen at random what is the probability that both books are fiction? (b) Six books are chosen at random. What is the probability that all six books are fiction? (c) What is the probability that at least one of six randomly selected books is non-fiction? Would it be unusual that at least one of six randomly selected books is non-fiction? (a) The probability is (b) The probability is (c) The probability is It would that at least one of six randomly selected books is non-fiction.

Explanation / Answer

Given,

P( Book classified as fiction ) = 0.89

a )

Two books are randomly selected.

P( Both books are fiction ) = 0.89*0.89 = 0.7921

B)

Six books are randomly selected.

P( All six books are fiction ) = ( 0.89 )6 = 0.4970

c)

P( at least one book is non-fiction ) = 1 - P( all books are fiction )

From part b ) P( all books are fiction ) = 0.4970

P( at least one book is non-fiction ) = 1 - 0.4970 = 0.503

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