1. The problem is to find the probability $p(X)$ of a random variable $X$. 2. The formula to find $p(X)$ depends on the context: if $X$ is discrete, $p(X=x)$ is the probability mass function (PMF) giving the probability that $X$ takes the value $x$. 3. For discrete variables, $p(X=x)$ satisfies $0 \leq p(X=x) \leq 1$ and $\sum_x p(X=x) = 1$. 4. For continuous variables, $p(X)$ is a probability density function (PDF), and probabilities are found by integrating: $P(a \leq X \leq b) = \int_a^b p(X) \, dX$. 5. To find $p(X)$, you need the distribution of $X$ or data to estimate it. 6. For example, if $X$ is binomial with parameters $n$ and $p$, then $p(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$. 7. Without more information, you cannot find a specific $p(X)$; you must know the distribution or have data. 8. In summary, $p(X)$ is the function that assigns probabilities to values of $X$ according to its distribution.