### Home > CC2 > Chapter 7 > Lesson 7.1.2 > Problem 7-25

Alan is making a bouquet to take home to his grandmother. He needs to choose one kind of greenery and one kind of flower for his bouquet. He has a choice of ferns or leaves for his greenery. His flower choices are daisies, carnations, and sunflowers.

Draw a tree diagram to show the different bouquets he could make. How many are there?

The first thing Alan must choose is the type of greenery. There are two choices, so your tree diagram should split into two branches. Two branches, labeled, ferns & leaves.

For each of those two choices, he must choose between three different types of flower. Draw each branch splitting into three different branches. The fern branch splits into daisies, carnations or sunflowers. The leaves branch splits into daisies, carnations or sunflowers.

There are six different possibilities.

What is the probability that he will use ferns?

A blue box is drawn around the entire top Fern branch. How many of the six possibilities contain ferns?

Count them using the tree diagram.

What is the probability that he will not use sunflowers?

Purple boxes, drawn around the two top branches, on the fern branch, and around the 2 top branches on the Leaves branch. Look at the diagram and see how many of the possibilities do not include sunflowers.

What is the probability that he will use leaves and carnations?

See part (b).