Convergence in probability is a concept in statistics and probability theory that describes how a sequence of random variables approaches a specific value as the number of observations increases. Specifically, a sequence of random variables X_n converges in probability to a random variable X if, for any small positive number ε, the probability that the difference between X_n and X exceeds ε approaches zero as n increases. This concept is important in the field of statistical inference and is often used in the context of law of large numbers. It helps in understanding how sample averages or estimates become more accurate as more data is collected, ensuring that the estimates are reliable in the long run.