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When dealing with probability, the term 'sample space' is fundamental. It represents all possible outcomes of a random experiment. Imagine a pot containing different colored balls; the sample space includes every ball you could possibly pick. In the context of the given exercise, the experiment is selecting a single-digit number. The single digits, ranging from 0 to 9, create a sample space comprising ten elements: \( \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\} \).

Clarifying the sample space before attempting to solve any probability problem is crucial because it provides a clear scope within which probabilities are calculated. Often misunderstood or incorrectly identified, the sample space is the bedrock upon which we determine the likelihood of any event, and understanding it helps avoid errors in further calculations.

To calculate probability, you need to understand its basic principle: it's the measure of how likely an event is to occur. The formula is straightforward: probability equals the number of favorable outcomes divided by the number of all possible outcomes in the sample space. In formula terms, it is \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).

Using the exercise as an illustration, we want to find the probability of selecting any single digit from the given sample space. As there is only one occurrence of each digit and ten possible digits, the probability for any given digit is \( \frac{1}{10} \), since each digit represents a single favorable outcome out of ten total outcomes. Remember, all outcomes are assumed to be equally probable. Grasping this core concept is essential to succeed in various probability questions, making it easier to predict the chance of occurrence of more complex events.

Let's focus on a common probability problem: finding the likelihood of drawing an even number. An even number is a number that can be divided by 2 without leaving a remainder. In our sample space, the even numbers are 0, 2, 4, 6, and 8.

To calculate the probability of picking an even number from the sample space, you count the even numbers, which in our case are 5. Then, use the total number of outcomes in the sample space, which is 10. The probability is the ratio of these two numbers, which simplifies to \( \frac{5}{10} = \frac{1}{2} \) or 50%. This tells us that we have an even chance, or a 'fifty-fifty' shot, at drawing an even number from the sample space. Understanding how to compute even number probability is useful not just in pure mathematics but also in real-world scenarios where decision-making can rely upon weighing out such chances.