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Question

A shelf has books with different-colored covers; 5 are blue, 6 are red, 1 is orange, 3 are white, and 1 is blue and white.

1.What is the probability of choosing a book that has either orange or white on its cover?

2.What is the probability of choosing a book that has either blue or white on its cover?

3.What is the probability of choosing a book with blue on its cover and replacing it before choosing a book with white on its cover?

Answer 1

(1) Choosing a book that has either orange or white on its cover:

There are 16 books total. There are 3 white, 1 orange and 1 with white (and blue) which totals 5. So the probability is 5/16.

(2) Choosing a book that either has blue or white (and I assume it can have both) on its cover:

5 books are blue, 3 are white and 1 is both blue and white. This yields a total of 9 books so the answer is 9/16.

(3) Choosing a book with blue on its cover and replacing it before choosing on with white:

The first part has a probability of 6/16 (5 blue books plus the one with blue and white) .This simplifies to 3/8.

The book is replaced. Then there are 3 white and the one with blue and white so the probability is 4/16 which simplifies to 1/4.

Your answer is the product of 3/8 and 1/4 which equals 3/32.