A **frequency tree** can be used to determine how many combinations of one or more events can take place. In its simplest form, a frequency tree consists of two branches.

Consider a bag of red and blue balls. If there are 6 red balls and 4 blue balls, the tree diagram will show:

The diagram shows that there are 6 ways to pick a red ball, and 4 ways to pick a blue ball.

If a red ball was picked and then placed back in the bag; and another ball was picked, the diagram could be extended:

The number of ways of picking a red ball, followed by another red ball is found by multiplying along the branches concerned: 6 x 6 = 36 ways of picking a red ball followed by another red ball.

If the ball is **not** replaced in the bag, then the number of red balls available for the second selection changes, and the number of ways of picking a red ball becomes 6 x 5 = 30 ways:

A bag of chocolates is offered to Amelia. In the bag there are 5 white chocolates, and 7 milk chocolates. Draw a frequency tree for Amelia as she selects her chocolate.

Answer:

Amelia chooses a chocolate, then replaces it in the bag. She then chooses again. How many different ways can she choose a white chocolate, followed by another white chocolate?

From the frequency tree, 5 x 5 = 25

Answer: 25

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