Q.Two cards are drawn at random, without replacement, from a well-shuffled deck of $52$ playing cards. Let $X$ denote the number of aces obtained. Find the probability distribution of $X$.

A random variable is a real-valued function defined on the sample space of a random experiment, assigning a single number to every outcome. A discrete random variable takes finitely many distinct values $x_1,\dots,x_n$, and its probability distribution is the table pairing each value with its probability $p_i=P(X=x_i)$. A valid probability distribution must satisfy two conditions: every $p_i\ge0$, and the probabilities sum to exactly $1$ ($\sum p_i=1$). Constr …