The probability that a continuous random variable equals a single number is zero because the probability distribution is spread over a continuous range, and the probability of any specific point in that range, having no width, is infinitesimally small, making $P(X = a) = 0$.

Would you like more details on this concept? Here are five related questions:

1. How does the probability density function (PDF) describe probabilities for continuous random variables?
2. What is the role of integration in finding probabilities over intervals for continuous random variables?
3. Can you compare discrete and continuous random variables in terms of probability calculations?
4. How does the concept of limits in calculus help explain the zero probability of specific values?
5. What is the significance of cumulative distribution functions (CDF) for continuous random variables?

Tip: For continuous random variables, probabilities are calculated over intervals, not at specific points, by integrating the probability density function over the desired range.