Question

A bookbook can be classified as either non dash fictionnon-fiction or fictionfiction. Suppose that 9494​% of booksbooks are classified as fictionfiction. ​(a) Two booksbooks are chosen at random. What is the probability that both booksbooks are fictionfiction​? ​(b) FiveFive booksbooks are chosen at random. What is the probability that all fivefive booksbooks are fictionfiction​? ​(c) What is the probability that at least one of fivefive randomly selected booksbooks is non dash fictionnon-fiction​? Would it be unusual that at least one of fivefive randomly selected booksbooks is non dash fictionnon-fiction​?

Answer 1

a) 0.8836

b) 0.7339

c) 0.2342

Explanation:

Books classified as fiction = 94% or 0.94 probability

Books classified as non-fiction = 1 - 0.94 = 0.06

a) for two books, we get: 0.94 * 0.94 = 0.8836 Probability

b) The probability that all five books are fiction is: 0.94^5

This equals 0.7339 Probability

c) Probability that one books is non-fiction, while the other 4 are fiction is determined in the following way:

Probability of non-fiction * probability of fiction^(number of books)

0.06 * 0.94^4 = 0.0468

This does not account for the order at which the non-fiction book shows up. Such as the non-fiction book being the first book picked, or in another case - the non-fiction book being the last picked.

Since there are 5 ways this could occur, the total probability will be calculated as shown: 0.0468 * 5 = 0.2342 Probability