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To create a tree diagram for flipping a coin three times, you can follow these steps:
1. Start by drawing three branches from the initial node representing the first coin flip.
2. Label the branches with the possible outcomes of the first flip: "Heads" and "Tails."
3. From each branch, extend two more branches to represent the second coin flip, resulting in a total of four branches at the second level.
4. Label these branches with the possible outcomes of the second flip: "Heads" and "Tails."
5. Repeat the process for the third coin flip, extending two branches from each of the four branches at the second level, resulting in eight branches at the third level.
6. Label these branches with the possible outcomes of the third flip: "Heads" and "Tails."
After creating the tree diagram following the steps above, you can list the outcomes in the sample space. The sample space for flipping a coin three times includes all the possible outcomes of the three coin flips:
1. (H, H, H) - Heads on all three flips
2. (H, H, T) - Heads on the first two flips, Tails on the third flip
3. (H, T, H) - Heads on the first and third flips, Tails on the second flip
4. (H, T, T) - Heads on the first flip, Tails on the second and third flips
5. (T, H, H) - Tails on the first flip, Heads on the second and third flips
6. (T, H, T) - Tails on the first and third flips, Heads on the second flip
7. (T, T, H) - Tails on the first two flips, Heads on the third flip
8. (T, T, T) - Tails on all three flips
These eight outcomes represent the sample space for flipping a coin three times. Each outcome corresponds to a specific sequence of Heads (H) and Tails (T) in the three coin flips.
