Final answer:
The probability of a specific outcome when flipping a fair coin is based on the principles of probability, including the binomial probability formula. The question involves finding the probability of a certain number of heads in multiple flips, which relates to a classic probability theory subject taught in high school mathematics.
Step-by-step explanation:
The probability of a specific outcome when flipping a fair coin multiple times depends on the rules of probability and combinations that arise from each flip. Since a fair coin has an equal chance of landing heads (H) or tails (T), each flip is an independent event with a probability of 0.5 for heads and a probability of 0.5 for tails. For instance, flipping a fair coin 14 times and calculating a specific outcome like getting exactly 7 heads will involve using the binomial probability formula, which takes into account the number of desired successes, the total number of trials, and the probability of success on each trial.
To calculate the probability of getting exactly 7 heads in 14 flips of a fair coin, we can use the formula P(X=k) = (n choose k) * p^k * (1-p)^(n-k) where 'n' is the number of trials, 'k' is the number of successes (heads in this case), and 'p' is the probability of getting heads on a single flip. Substituting the values to get the probability of exactly 7 heads, we would have P(X=7) = (14 choose 7) * (0.5)^7 * (0.5)^(14-7).
This topic in probability theory assists in understanding how the likelihood of various outcomes can be calculated and how frequent certain results might be expected. This extends to areas such as statistical analysis and predicting events based on known probabilities, adhering to the principles outlined in the law of large numbers as illustrated by Karl Pearson.