Probability of Consecutive Coin Flips

What’s the probability of flipping heads three times in a row?

This problem explores a fundamental concept in probability: the likelihood of independent events occurring in sequence. When faced with determining the probability of flipping heads three times consecutively, it's important to understand the concept of independent and identically distributed events. Coin flips are a classic example where each flip doesn't depend on the previous one, and each side of the coin is equally likely, assuming a fair coin.

To solve this type of problem, one must consider the probability of each individual event happening and then combine these probabilities because they are independent events. This is done through multiplication of the probabilities of individual events. This problem is a good exercise in applying the multiplication rule for independent events, which states that you can find the probability of two or more independent events all occurring by multiplying their individual probabilities.

Conceptually, this problem connects to broader themes of probabilistic thinking that underpin many aspects of statistics, including how to handle multiple trials and sequences of events. It serves as a stepping stone to more complex topics like Markov processes and probabilistic models where the underlying mechanics remain essential for deeper understanding.