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A probability distribution describes how the probabilities of a random variable are distributed across its possible values. In this case, the random variable x represents the number of matching digits in the lottery, and the table provides the probabilities for each possible outcome (0 to 4 matches). Understanding this distribution is essential for calculating specific probabilities, such as the likelihood of getting exactly 2 matches.

A random variable is a numerical outcome of a random phenomenon. In the context of the lottery, the random variable x quantifies the number of digits that match the drawn numbers in the correct order. Recognizing how random variables operate helps in analyzing the probabilities associated with different outcomes, which is crucial for solving the given problem.

Calculating probabilities involves determining the likelihood of a specific event occurring based on a probability distribution. For this question, to find the probability of getting exactly 2 matches, one would refer to the provided table and identify the corresponding probability value, which is 0.049. This process is fundamental in statistics for making informed predictions and decisions based on random events.