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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Mathematics

Sean Conner

Yesterday, 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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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