To determine the probability that all three flips of a coin will be the same, we first need to consider the possible outcomes of the flips. When flipping a coin, there are two potential results for each flip: heads (H) or tails (T).
For three flips, the total number of possible outcomes is calculated as follows:
- Each flip has 2 outcomes (H or T).
- For three flips: 2 x 2 x 2 = 23 = 8 possible outcomes.
The possible outcomes for three flips are:
- HHH
- HHT
- HTH
- THH
- HTT
- THT
- TTH
- TTT
Out of these outcomes, only two combinations result in all three flips being the same: HHH and TTT.
Now, we can find the probability as the ratio of the number of successful outcomes (where all flips are the same) to the total number of outcomes:
Probability = (Number of successful outcomes) / (Total number of outcomes)
Thus, it is:
Probability = 2 / 8 = 1 / 4 = 0.25
Therefore, the probability that all three coin flips will be the same is 0.25 or 25%.