For a missing category in a probability problem, use the complement: the share left after the known categories. If the categories cover the whole group without overlap, their probabilities add to . Find the missing share, then multiply it by the total count in Desmos. Don’t subtract probabilities directly from a count; shares and counts are different kinds of numbers.
Hints
- Hint 1
The complement is everything left outside the named categories. Each book belongs to one of three categories. What share of the whole remains after you remove fiction and nonfiction?
- Hint 2
A probability is a share of all the books, not a book count. Once you find the children’s share, what operation turns it into a count out of ?
Step-by-step
Find the missing share, then the count
Step 1Write the children’s share
Because every book is in exactly one of the three categories, their probabilities add to . The complement of fiction or nonfiction means neither category, which here is children’s. So the probability, or share of all books, is . Subtract from the whole probability, not from books.
- Step 2
Find the remaining share
Type into Desmos. It shows , so children’s books make up of the shipment. That’s a probability, not yet a number of books.
- Step 3
Turn the share into a book count
A category’s probability is its count divided by the total, so multiply its share by the full shipment of books. Type in Desmos; it shows . There are children’s books. Grid in 72.