Q13. - Algebra 1

Question

Use a tree diagram to find the sample space for each event. State the number of possible outcomes.

How many different 3 -character codes are there using A, B, or C for the first character, 8 or 9 for the second character, and 0 or 1 for the third character?

Step-by-Step Solution

Answer

The total number of possible outcomes choosing three different characters for code is 12.

Step 1. Define a tree diagram.

A tree diagram is a way to display all the possible outcomes of an event. Each branch of the tree diagram of any event represents a possible outcome for that event.

Step 2. Plot tree diagram.

As the code is of 3-characters and the first character has three choices (A, B, or C), the second character has two choices(8, or 9) and the third character has two choices(0, or 1).

Thus, the tree diagram for 3-character code is:

Step 3. Count the total possible outcomes.

Using the tree diagram in the above step it can be noticed that the total number of possible outcomes choosing three different characters for code is 12.