To determine which sequence of coin flips is the most consistent with an unbiased coin, we need to analyze how well each sequence approximates an equal number of heads (H) and tails (T). An unbiased coin should ideally have a roughly equal count of heads and tails because both outcomes are equally likely.
Let's analyze each sequence:
1. Sequence 1: H H T T T T H T H T T T
- Heads (H) count: 4
- Tails (T) count: 8
- Difference: |4 - 8| = 4
2. Sequence 2: H T T T H T T T T H T T
- Heads (H) count: 3
- Tails (T) count: 9
- Difference: |3 - 9| = 6
3. Sequence 3: T H T H T T T H T T H H
- Heads (H) count: 5
- Tails (T) count: 7
- Difference: |5 - 7| = 2
4. Sequence 4: H H H T T H T T H H H H
- Heads (H) count: 8
- Tails (T) count: 4
- Difference: |8 - 4| = 4
The sequence with the smallest difference between the count of heads and tails is the most consistent with an unbiased coin. Here's a summary of the differences:
- Sequence 1: 4
- Sequence 2: 6
- Sequence 3: 2
- Sequence 4: 4
The sequence with the smallest difference is Sequence 3, with a difference of 2.
Therefore, the most consistent sequence with an unbiased coin is:
T H T H T T T H T T H H.
