Of all the books at a certain library, if you select one at random, then there is a 90% chance that it has illustrations. Of all the illustrations in all the books, if you select one at random, then there is a 90% chance that it is in color. If the library has 10,000 books, then what is the minimum number of books that must contain colored illustrations?

Question

Mathematics

Sean Conner

16 October, 22:02

Of all the books at a certain library, if you select one at random, then there is a 90% chance that it has illustrations. Of all the illustrations in all the books, if you select one at random, then there is a 90% chance that it is in color. If the library has 10,000 books, then what is the minimum number of books that must contain colored illustrations?

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Answers (1)

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Bianca Todd · Answer 1

There will be a minimum of 8,100 books with coloured illustrations.

Step-by-step explanation:

Change the percentages to fractions

90% = 9/10

Books with Illustrations: 9/10 of 10,000

Books in Colour: 9/10 of 10,000

Because both events are not mutually exclusive, they can happen at the same time. So multiply their fractions (probabilities).

9/10 * 9/10 =

9 * 9 = 81

10 * 10 = 100

The probability of having a book with coloured illustrations is 81/100.

Find this as a fraction of 10000.

10000 : 100 * 81 = 8,100