The spinner shown is spun twice. Use a tree diagram to record the sample space of the repeated experiment.
The spinner shown is spun twice. Use a tree diagram to record the sample space of the repeated experiment.
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To create a tree diagram for a spinner spun twice, follow these steps:
1. Identify Outcomes of One Spin: Assume the spinner has sections labeled A, B, and C. This means one spin can result in either A, B, or C.
2. First Spin: Create the first level of the tree with three branches, one for each outcome: A, B, and C.
3. Second Spin: From each outcome of the first spin, draw three branches for the second spin (again resulting in A, B, or C).
4. Complete the Tree: For each outcome from the first spin, there will be three branches representing the possible outcomes from the second spin.
The complete tree will look like this:
– First Spin:
– A → Second Spin:
– A (AA)
– B (AB)
– C (AC)
– B → Second Spin:
– A (BA)
– B (BB)
– C (BC)
– C → Second Spin:
– A (CA)
– B (CB)
– C (CC)
5. Sample Space: The sample space, which is the set of all possible outcomes, will be: {AA, AB, AC, BA, BB, BC, CA, CB, CC}.
This diagram helps visualize all the combinations that can occur when the spinner is spun twice. If you need more assistance