When flipping a fair coin, there are two possible outcomes for each flip: heads (H) or tails (T). If we want to determine the probability that all three flips result in the same outcome, we can analyze the possible scenarios.
For three flips, the total number of possible outcomes can be calculated as:
2 choices (H or T) raised to the power of 3 flips = 23 = 8 possible outcomes.
These outcomes are:
- HHH
- HHT
- HTH
- THH
- TTT
- TTH
- THT
- HTT
Out of these 8 outcomes, only two meet our criteria of having all three flips being the same:
- HHH
- TTT
Therefore, the probability of all three flips resulting in the same outcome is calculated by taking the number of successful outcomes and dividing it by the total number of outcomes:
Probability = (Number of Successful Outcomes) / (Total Number of Outcomes) = 2 / 8 = 1 / 4.
So, the probability that all three flips will be the same is 1/4 or 25%.