Make a tree diagram to show all the possible outcomes of flipping a coin 5 times. How many outcomes are there?
To create a tree diagram for flipping a coin 5 times, we can use the branches to represent the two possible outcomes (heads or tails) for each flip.
Starting with the first flip:
- Heads (H) - Tails (T)
For the second flip:
- H-H, H-T, T-H, T-T
For the third flip:
- H-H-H, H-H-T, H-T-H, H-T-T, T-H-H, T-H-T, T-T-H, T-T-T
For the fourth flip:
- H-H-H-H, H-H-H-T, H-H-T-H, H-H-T-T, H-T-H-H, H-T-H-T, H-T-T-H, H-T-T-T, T-H-H-H, T-H-H-T, T-H-T-H, T-H-T-T, T-T-H-H, T-T-H-T, T-T-T-H, T-T-T-T
For the fifth flip:
- 32 possible outcomes for fifth flip
So, there are a total of 2^5 = 32 outcomes for flipping a coin 5 times.