Each child in a family of 3 children is going to get a pet. One wants a dog or cat, another wants a bird or rabbit, and the third wants a frog or snake. List a sample space or draw a tree diagram and determine the number of possible outcomes.
To determine the sample space and the number of possible outcomes, we can create a tree diagram.
First, let's list down the choices for each child:
- Child 1: Dog or Cat
- Child 2: Bird or Rabbit
- Child 3: Frog or Snake
Now, we can start by drawing the first layer of the tree diagram, representing the choices of the first child:
/ \
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Dog Cat
Next, we draw the second layer of the tree diagram, representing the choices of the second child for each of the first child's choices:
/ \ / \
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Bird Rabbit Bird Rabbit
Lastly, we draw the third layer of the tree diagram, representing the choices of the third child for each combination of the first two children's choices:
/ \ / \ / \ / \
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Frog Snake Frog Snake Frog Snake Frog Snake
Now, let's count the number of possible outcomes. By looking at the tree diagram, we can see that each branch represents one possible choice made by each child. The number of branches in each layer represents the number of choices available for that child.
In this case, the first child has 2 choices, the second child has 2 choices, and the third child also has 2 choices. Therefore, the total number of possible outcomes is calculated by multiplying the number of choices for each child: 2 * 2 * 2 = 8.
So, the sample space or the number of possible outcomes is 8.